Search | arXiv e-print repository

<!DOCTYPE html> <html lang="en"> <head> <meta charset="utf-8"/> <meta name="viewport" content="width=device-width, initial-scale=1"/>  <link rel="apple-touch-icon" sizes="180x180" href="https://static.arxiv.org/static/base/1.0.0a5/images/icons/apple-touch-icon.png"> <link rel="icon" type="image/png" sizes="32x32" href="https://static.arxiv.org/static/base/1.0.0a5/images/icons/favicon-32x32.png"> <link rel="icon" type="image/png" sizes="16x16" href="https://static.arxiv.org/static/base/1.0.0a5/images/icons/favicon-16x16.png"> <link rel="manifest" href="https://static.arxiv.org/static/base/1.0.0a5/images/icons/site.webmanifest"> <link rel="mask-icon" href="https://static.arxiv.org/static/base/1.0.0a5/images/icons/safari-pinned-tab.svg" color="#b31b1b"> <link rel="shortcut icon" href="https://static.arxiv.org/static/base/1.0.0a5/images/icons/favicon.ico"> <meta name="msapplication-TileColor" content="#b31b1b"> <meta name="msapplication-config" content="images/icons/browserconfig.xml"> <meta name="theme-color" content="#b31b1b">  <title>Search | arXiv e-print repository</title> <script defer src="https://static.arxiv.org/static/base/1.0.0a5/fontawesome-free-5.11.2-web/js/all.js"></script> <link rel="stylesheet" href="https://static.arxiv.org/static/base/1.0.0a5/css/arxivstyle.css" /> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ messageStyle: "none", extensions: ["tex2jax.js"], jax: ["input/TeX", "output/HTML-CSS"], tex2jax: { inlineMath: [ ['$','$'], ["\$","\$"] ], displayMath: [ ['$$','$$'], ["\\[","\\]"] ], processEscapes: true, ignoreClass: '.*', processClass: 'mathjax.*' }, TeX: { extensions: ["AMSmath.js", "AMSsymbols.js", "noErrors.js"], noErrors: { inlineDelimiters: ["$","$"], multiLine: false, style: { "font-size": "normal", "border": "" } } }, "HTML-CSS": { availableFonts: ["TeX"] } }); </script> <script src='//static.arxiv.org/MathJax-2.7.3/MathJax.js'></script> <script src="https://static.arxiv.org/static/base/1.0.0a5/js/notification.js"></script> <link rel="stylesheet" href="https://static.arxiv.org/static/search/0.5.6/css/bulma-tooltip.min.css" /> <link rel="stylesheet" href="https://static.arxiv.org/static/search/0.5.6/css/search.css" /> <script src="https://code.jquery.com/jquery-3.2.1.slim.min.js" integrity="sha256-k2WSCIexGzOj3Euiig+TlR8gA0EmPjuc79OEeY5L45g=" crossorigin="anonymous"></script> <script src="https://static.arxiv.org/static/search/0.5.6/js/fieldset.js"></script> <style> radio#cf-customfield_11400 { display: none; } </style> </head> <body> <header><a href="#main-container" class="is-sr-only">Skip to main content</a>  <div class="attribution level is-marginless" role="banner"> <div class="level-left"> <a class="level-item" href="https://cornell.edu/"><img src="https://static.arxiv.org/static/base/1.0.0a5/images/cornell-reduced-white-SMALL.svg" alt="Cornell University" width="200" aria-label="logo" /></a> </div> <div class="level-right is-marginless"><p class="sponsors level-item is-marginless"><span id="support-ack-url">We gratefully acknowledge support from<br /> the Simons Foundation, <a href="https://info.arxiv.org/about/ourmembers.html">member institutions</a>, and all contributors. <a href="https://info.arxiv.org/about/donate.html">Donate</a></span></p></div> </div>  <div class="identity level is-marginless"> <div class="level-left"> <div class="level-item"> <a class="arxiv" href="https://arxiv.org/" aria-label="arxiv-logo"> <img src="https://static.arxiv.org/static/base/1.0.0a5/images/arxiv-logo-one-color-white.svg" aria-label="logo" alt="arxiv logo" width="85" style="width:85px;"/> </a> </div> </div> <div class="search-block level-right"> <form class="level-item mini-search" method="GET" action="https://arxiv.org/search"> <div class="field has-addons"> <div class="control"> <input class="input is-small" type="text" name="query" placeholder="Search..." aria-label="Search term or terms" /> <p class="help"><a href="https://info.arxiv.org/help">Help</a> | <a href="https://arxiv.org/search/advanced">Advanced Search</a></p> </div> <div class="control"> <div class="select is-small"> <select name="searchtype" aria-label="Field to search"> <option value="all" selected="selected">All fields</option> <option value="title">Title</option> <option value="author">Author</option> <option value="abstract">Abstract</option> <option value="comments">Comments</option> <option value="journal_ref">Journal reference</option> <option value="acm_class">ACM classification</option> <option value="msc_class">MSC classification</option> <option value="report_num">Report number</option> <option value="paper_id">arXiv identifier</option> <option value="doi">DOI</option> <option value="orcid">ORCID</option> <option value="author_id">arXiv author ID</option> <option value="help">Help pages</option> <option value="full_text">Full text</option> </select> </div> </div> <input type="hidden" name="source" value="header"> <button class="button is-small is-cul-darker">Search</button> </div> </form> </div> </div>  <div class="container"> <div class="user-tools is-size-7 has-text-right has-text-weight-bold" role="navigation" aria-label="User menu"> <a href="https://arxiv.org/login">Login</a> </div> </div> </header> <main class="container" id="main-container"> <div class="level is-marginless"> <div class="level-left"> <h1 class="title is-clearfix"> Showing 1–28 of 28 results for author: <span class="mathjax">Li, G</span> </h1> </div> <div class="level-right is-hidden-mobile">  <span class="help" style="display: inline-block;"><a href="https://github.com/arXiv/arxiv-search/releases">Search v0.5.6 released 2020-02-24</a>  </span> </div> </div> <div class="content"> <form method="GET" action="/search/math-ph" aria-role="search"> Searching in archive <strong>math-ph</strong>. <a href="/search/?searchtype=author&query=Li%2C+G">Search in all archives.</a> <div class="field has-addons-tablet"> <div class="control is-expanded"> <label for="query" class="hidden-label">Search term or terms</label> <input class="input is-medium" id="query" name="query" placeholder="Search term..." type="text" value="Li, G"> </div> <div class="select control is-medium"> <label class="is-hidden" for="searchtype">Field</label> <select class="is-medium" id="searchtype" name="searchtype"><option value="all">All fields</option><option value="title">Title</option><option selected value="author">Author(s)</option><option value="abstract">Abstract</option><option value="comments">Comments</option><option value="journal_ref">Journal reference</option><option value="acm_class">ACM classification</option><option value="msc_class">MSC classification</option><option value="report_num">Report number</option><option value="paper_id">arXiv identifier</option><option value="doi">DOI</option><option value="orcid">ORCID</option><option value="license">License (URI)</option><option value="author_id">arXiv author ID</option><option value="help">Help pages</option><option value="full_text">Full text</option></select> </div> <div class="control"> <button class="button is-link is-medium">Search</button> </div> </div> <div class="field"> <div class="control is-size-7"> <label class="radio"> <input checked id="abstracts-0" name="abstracts" type="radio" value="show"> Show abstracts </label> <label class="radio"> <input id="abstracts-1" name="abstracts" type="radio" value="hide"> Hide abstracts </label> </div> </div> <div class="is-clearfix" style="height: 2.5em"> <div class="is-pulled-right"> <a href="/search/advanced?terms-0-term=Li%2C+G&terms-0-field=author&size=50&order=-announced_date_first">Advanced Search</a> </div> </div> <input type="hidden" name="order" value="-announced_date_first"> <input type="hidden" name="size" value="50"> </form> <div class="level breathe-horizontal"> <div class="level-left"> <form method="GET" action="/search/"> <div style="display: none;"> <select id="searchtype" name="searchtype"><option value="all">All fields</option><option value="title">Title</option><option selected value="author">Author(s)</option><option value="abstract">Abstract</option><option value="comments">Comments</option><option value="journal_ref">Journal reference</option><option value="acm_class">ACM classification</option><option value="msc_class">MSC classification</option><option value="report_num">Report number</option><option value="paper_id">arXiv identifier</option><option value="doi">DOI</option><option value="orcid">ORCID</option><option value="license">License (URI)</option><option value="author_id">arXiv author ID</option><option value="help">Help pages</option><option value="full_text">Full text</option></select> <input id="query" name="query" type="text" value="Li, G"> <ul id="abstracts"><li><input checked id="abstracts-0" name="abstracts" type="radio" value="show"> <label for="abstracts-0">Show abstracts</label></li><li><input id="abstracts-1" name="abstracts" type="radio" value="hide"> <label for="abstracts-1">Hide abstracts</label></li></ul> </div> <div class="box field is-grouped is-grouped-multiline level-item"> <div class="control"> <span class="select is-small"> <select id="size" name="size"><option value="25">25</option><option selected value="50">50</option><option value="100">100</option><option value="200">200</option></select> </span> <label for="size">results per page</label>. </div> <div class="control"> <label for="order">Sort results by</label> <span class="select is-small"> <select id="order" name="order"><option selected value="-announced_date_first">Announcement date (newest first)</option><option value="announced_date_first">Announcement date (oldest first)</option><option value="-submitted_date">Submission date (newest first)</option><option value="submitted_date">Submission date (oldest first)</option><option value="">Relevance</option></select> </span> </div> <div class="control"> <button class="button is-small is-link">Go</button> </div> </div> </form> </div> </div> <ol class="breathe-horizontal" start="1"> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2503.01267">arXiv:2503.01267</a> <span> [<a href="https://arxiv.org/pdf/2503.01267">pdf</a>, <a href="https://arxiv.org/ps/2503.01267">ps</a>, <a href="https://arxiv.org/format/2503.01267">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Exactly Solvable and Integrable Systems">nlin.SI</span> </div> </div> <p class="title is-5 mathjax"> Riemann-Hilbert approach to the Algebro-Geometric solution of the modified Camassa-Holm equation with linear dispersion term </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Fan%2C+E">Engui Fan</a>, <a href="/search/math-ph?searchtype=author&query=Li%2C+G">Gaozhan Li</a>, <a href="/search/math-ph?searchtype=author&query=Yang%2C+Y">Yiling Yang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2503.01267v1-abstract-short" style="display: inline;"> This paper aims at providing an exact algebro-geometric solution of the modified Camassa-Holm (mCH) equation derived from hyperelliptic curves in $4(p+q)-1$ genus. To achieve this goal, we construct the Riemann-Hilbert problems cosponsoring to the mCH equation, which can be solved exactly by the Baker-Akhiezer function. Then the precise expression of the algebro-geometric solution of the mCH equat… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.01267v1-abstract-full').style.display = 'inline'; document.getElementById('2503.01267v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2503.01267v1-abstract-full" style="display: none;"> This paper aims at providing an exact algebro-geometric solution of the modified Camassa-Holm (mCH) equation derived from hyperelliptic curves in $4(p+q)-1$ genus. To achieve this goal, we construct the Riemann-Hilbert problems cosponsoring to the mCH equation, which can be solved exactly by the Baker-Akhiezer function. Then the precise expression of the algebro-geometric solution of the mCH equation can be obtained through reconstructed formula. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.01267v1-abstract-full').style.display = 'none'; document.getElementById('2503.01267v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 3 March, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2025. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2409.06905">arXiv:2409.06905</a> <span> [<a href="https://arxiv.org/pdf/2409.06905">pdf</a>, <a href="https://arxiv.org/format/2409.06905">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Analysis of PDEs">math.AP</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Probability">math.PR</span> </div> </div> <p class="title is-5 mathjax"> Deep-water and shallow-water limits of statistical equilibria for the intermediate long wave equation </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Chapouto%2C+A">Andreia Chapouto</a>, <a href="/search/math-ph?searchtype=author&query=Li%2C+G">Guopeng Li</a>, <a href="/search/math-ph?searchtype=author&query=Oh%2C+T">Tadahiro Oh</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2409.06905v1-abstract-short" style="display: inline;"> We study the construction of invariant measures associated with higher order conservation laws of the intermediate long wave equation (ILW) and their convergence properties in the deep-water and shallow-water limits. By exploiting its complete integrability, we first carry out detailed analysis on the construction of appropriate conservation laws of ILW at the $H^\frac k2$-level for each… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2409.06905v1-abstract-full').style.display = 'inline'; document.getElementById('2409.06905v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2409.06905v1-abstract-full" style="display: none;"> We study the construction of invariant measures associated with higher order conservation laws of the intermediate long wave equation (ILW) and their convergence properties in the deep-water and shallow-water limits. By exploiting its complete integrability, we first carry out detailed analysis on the construction of appropriate conservation laws of ILW at the $H^\frac k2$-level for each $k \in \mathbb{N}$, and establish their convergence to those of the Benjamin-Ono equation (BO) in the deep-water limit and to those of the Korteweg-de Vries equation (KdV) in the shallow-water limit. In particular, in the shallow-water limit, we prove rather striking 2-to-1 collapse of the conservation laws of ILW to those of KdV. Such 2-to-1 collapse is novel in the literature and, to our knowledge, this is the first construction of a complete family of shallow-water conservation laws with non-trivial shallow-water limits. We then construct an infinite sequence of generalized Gibbs measures for ILW associated with these conservation laws and prove their convergence to the corresponding (invariant) generalized Gibbs measures for BO and KdV in the respective limits. Finally, for $k \ge 3$, we establish invariance of these measures under ILW dynamics, and also convergence in the respective limits of the ILW dynamics at each equilibrium state to the corresponding invariant dynamics for BO and KdV constructed by Deng, Tzvetkov, and Visciglia (2010-2015) and Zhidkov (1996), respectively. In particular, in the shallow-water limit, we establish 2-to-1 collapse at the level of the generalized Gibbs measures as well as the invariant ILW dynamics. As a byproduct of our analysis, we also prove invariance of the generalized Gibbs measure associated with the $H^2$-conservation law of KdV, which seems to be missing in the literature. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2409.06905v1-abstract-full').style.display = 'none'; document.getElementById('2409.06905v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 10 September, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">113 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 35Q35; 35Q53; 37K10; 60H30 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2408.04201">arXiv:2408.04201</a> <span> [<a href="https://arxiv.org/pdf/2408.04201">pdf</a>, <a href="https://arxiv.org/ps/2408.04201">ps</a>, <a href="https://arxiv.org/format/2408.04201">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Exactly Solvable and Integrable Systems">nlin.SI</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.nuclphysb.2024.116777">10.1016/j.nuclphysb.2024.116777 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Exact solution of a quantum integrable system associated with the $G_2$ exceptional Lie algebra </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Li%2C+G">Guang-Liang Li</a>, <a href="/search/math-ph?searchtype=author&query=Cao%2C+J">Junpeng Cao</a>, <a href="/search/math-ph?searchtype=author&query=Sun%2C+P">Pei Sun</a>, <a href="/search/math-ph?searchtype=author&query=Yang%2C+W">Wen-Li Yang</a>, <a href="/search/math-ph?searchtype=author&query=Shi%2C+K">Kangjie Shi</a>, <a href="/search/math-ph?searchtype=author&query=Wang%2C+Y">Yupeng Wang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2408.04201v3-abstract-short" style="display: inline;"> A quantum integrable spin chain model associated with the $G_2$ exceptional Lie algebra is studied. By using the fusion technique, the closed recursive relations among the fused transfer matrices are obtained. These identities allow us to derive the exact energy spectrum and Bethe ansatz equations of the system based on polynomial analysis. The present method provides a unified treatment to invest… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2408.04201v3-abstract-full').style.display = 'inline'; document.getElementById('2408.04201v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2408.04201v3-abstract-full" style="display: none;"> A quantum integrable spin chain model associated with the $G_2$ exceptional Lie algebra is studied. By using the fusion technique, the closed recursive relations among the fused transfer matrices are obtained. These identities allow us to derive the exact energy spectrum and Bethe ansatz equations of the system based on polynomial analysis. The present method provides a unified treatment to investigate the Bethe ansatz solutions for both periodic and non-diagonal open boundary conditions associated with exceptional Lie algebras. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2408.04201v3-abstract-full').style.display = 'none'; document.getElementById('2408.04201v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 16 December, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 7 August, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Some numerical checks for small site numbers are added; 36 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Nucl. Phys. B 1010 (2025), 116777 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2310.08783">arXiv:2310.08783</a> <span> [<a href="https://arxiv.org/pdf/2310.08783">pdf</a>, <a href="https://arxiv.org/ps/2310.08783">ps</a>, <a href="https://arxiv.org/format/2310.08783">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Probability">math.PR</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Analysis of PDEs">math.AP</span> </div> </div> <p class="title is-5 mathjax"> Optimal divergence rate of the focusing Gibbs measure </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Li%2C+G">Guopeng Li</a>, <a href="/search/math-ph?searchtype=author&query=Liang%2C+R">Rui Liang</a>, <a href="/search/math-ph?searchtype=author&query=Wang%2C+Y">Yuzhao Wang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2310.08783v1-abstract-short" style="display: inline;"> We study the focusing Gibbs measure with critical/supercritical potentials. In particular, we prove asymptotic formulae for the frequency approximation of the partition function, which captures the optimal divergence rate of the partition function as the frequency truncation is removed. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2310.08783v1-abstract-full" style="display: none;"> We study the focusing Gibbs measure with critical/supercritical potentials. In particular, we prove asymptotic formulae for the frequency approximation of the partition function, which captures the optimal divergence rate of the partition function as the frequency truncation is removed. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2310.08783v1-abstract-full').style.display = 'none'; document.getElementById('2310.08783v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 12 October, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">15 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 60H30; 81T08; 35Q55; 60H40 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2304.01935">arXiv:2304.01935</a> <span> [<a href="https://arxiv.org/pdf/2304.01935">pdf</a>, <a href="https://arxiv.org/ps/2304.01935">ps</a>, <a href="https://arxiv.org/format/2304.01935">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.nuclphysb.2023.116147">10.1016/j.nuclphysb.2023.116147 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Exact solution of the $q$-deformed $D^{(1)}_3$ vertex model with open boundaries </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Li%2C+G">Guang-Liang Li</a>, <a href="/search/math-ph?searchtype=author&query=Cao%2C+J">Junpeng Cao</a>, <a href="/search/math-ph?searchtype=author&query=Qiao%2C+Y">Yi Qiao</a>, <a href="/search/math-ph?searchtype=author&query=Yang%2C+W">Wen-Li Yang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2304.01935v1-abstract-short" style="display: inline;"> In this paper, we study the exact solution of the $q$-deformed $D^{(1)}_3$ quantum lattice model with non-diagonal open boundary condition. We demonstrate the crossing symmetry of the transfer matrix and obtain the quantum determinant. We construct the independent transfer matrix fusion identities and show that the fusion processes can be closed. Based on the fusion hierarchies and polynomial anal… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2304.01935v1-abstract-full').style.display = 'inline'; document.getElementById('2304.01935v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2304.01935v1-abstract-full" style="display: none;"> In this paper, we study the exact solution of the $q$-deformed $D^{(1)}_3$ quantum lattice model with non-diagonal open boundary condition. We demonstrate the crossing symmetry of the transfer matrix and obtain the quantum determinant. We construct the independent transfer matrix fusion identities and show that the fusion processes can be closed. Based on the fusion hierarchies and polynomial analysis, we obtain the inhomogeneous $T-Q$ relations, exact energy spectrum and Bethe ansatz equations of the system. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2304.01935v1-abstract-full').style.display = 'none'; document.getElementById('2304.01935v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 4 April, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">10 pages, 0 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Nuclear Physics B 989 (2023) 116147 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2303.16787">arXiv:2303.16787</a> <span> [<a href="https://arxiv.org/pdf/2303.16787">pdf</a>, <a href="https://arxiv.org/format/2303.16787">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Numerical Analysis">math.NA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> </div> <p class="title is-5 mathjax"> Dispersion relation reconstruction for 2D Photonic Crystals based on polynomial interpolation </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Wang%2C+Y">Yueqi Wang</a>, <a href="/search/math-ph?searchtype=author&query=Li%2C+G">Guanglian Li</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2303.16787v3-abstract-short" style="display: inline;"> Dispersion relation reflects the dependence of wave frequency on its wave vector when the wave passes through certain material. It demonstrates the properties of this material and thus it is critical. However, dispersion relation reconstruction is very time consuming and expensive. To address this bottleneck, we propose in this paper an efficient dispersion relation reconstruction scheme based on… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2303.16787v3-abstract-full').style.display = 'inline'; document.getElementById('2303.16787v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2303.16787v3-abstract-full" style="display: none;"> Dispersion relation reflects the dependence of wave frequency on its wave vector when the wave passes through certain material. It demonstrates the properties of this material and thus it is critical. However, dispersion relation reconstruction is very time consuming and expensive. To address this bottleneck, we propose in this paper an efficient dispersion relation reconstruction scheme based on global polynomial interpolation for the approximation of 2D photonic band functions. Our method relies on the fact that the band functions are piecewise analytic with respect to the wave vector in the first Brillouin zone. We utilize suitable sampling points in the first Brillouin zone at which we solve the eigenvalue problem involved in the band function calculation, and then employ Lagrange interpolation to approximate the band functions on the whole first Brillouin zone. Numerical results show that our proposed methods can significantly improve the computational efficiency. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2303.16787v3-abstract-full').style.display = 'none'; document.getElementById('2303.16787v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 27 October, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 29 March, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">27 pages, 14 figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2211.03243">arXiv:2211.03243</a> <span> [<a href="https://arxiv.org/pdf/2211.03243">pdf</a>, <a href="https://arxiv.org/ps/2211.03243">ps</a>, <a href="https://arxiv.org/format/2211.03243">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Analysis of PDEs">math.AP</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Probability">math.PR</span> </div> </div> <p class="title is-5 mathjax"> On the deep-water and shallow-water limits of the intermediate long wave equation from a statistical viewpoint </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Li%2C+G">Guopeng Li</a>, <a href="/search/math-ph?searchtype=author&query=Oh%2C+T">Tadahiro Oh</a>, <a href="/search/math-ph?searchtype=author&query=Zheng%2C+G">Guangqu Zheng</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2211.03243v2-abstract-short" style="display: inline;"> (Due to the limit on the number of characters for an abstract set by arXiv, the full abstract can not be displayed here. See the abstract in the paper.) We study convergence problems for the intermediate long wave equation (ILW), with the depth parameter $未> 0$, in the deep-water limit ($未\to \infty$) and the shallow-water limit ($未\to 0$) from a statistical point of view. In particular, we establ… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2211.03243v2-abstract-full').style.display = 'inline'; document.getElementById('2211.03243v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2211.03243v2-abstract-full" style="display: none;"> (Due to the limit on the number of characters for an abstract set by arXiv, the full abstract can not be displayed here. See the abstract in the paper.) We study convergence problems for the intermediate long wave equation (ILW), with the depth parameter $未> 0$, in the deep-water limit ($未\to \infty$) and the shallow-water limit ($未\to 0$) from a statistical point of view. In particular, we establish convergence of invariant Gibbs dynamics for ILW in both the deep-water and shallow-water limits. For this purpose, we first construct the Gibbs measures for ILW, $0 < 未< \infty$. As they are supported on distributions, a renormalization is required. With the Wick renormalization, we carry out the construction of the Gibbs measures for ILW. We then prove that the Gibbs measures for ILW converge in total variation to that for the Benjamin-Ono equation (BO) in the deep-water limit. In the shallow-water regime, after applying a scaling transformation, we prove that, as $未\to 0$, the Gibbs measures for the scaled ILW converge weakly to that for the Korteweg-de Vries equation (KdV). We point out that this second result is of particular interest since the Gibbs measures for the scaled ILW and KdV are mutually singular (whereas the Gibbs measures for ILW and BO are equivalent). We also discuss convergence of the associated dynamical problem. Lastly, we point out that our results also apply to the generalized ILW equation in the defocusing case, converging to the generalized BO in the deep-water limit and to the generalized KdV in the shallow-water limit. In the non-defocusing case, however, our results can not be extended to a nonlinearity with a higher power due to the non-normalizability of the corresponding Gibbs measures. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2211.03243v2-abstract-full').style.display = 'none'; document.getElementById('2211.03243v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 12 December, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 6 November, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">76 pages. Minor updates. To appear in Trans. London Math. Soc</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 35Q35; 60F15; 60H30 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2205.10818">arXiv:2205.10818</a> <span> [<a href="https://arxiv.org/pdf/2205.10818">pdf</a>, <a href="https://arxiv.org/ps/2205.10818">ps</a>, <a href="https://arxiv.org/format/2205.10818">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Exactly Solvable and Integrable Systems">nlin.SI</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.nuclphysb.2022.115946">10.1016/j.nuclphysb.2022.115946 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Exact surface energy of the $D^{(1)}_2$ spin chain with generic non-diagonal boundary reflections </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Li%2C+G">Guang-Liang Li</a>, <a href="/search/math-ph?searchtype=author&query=Qiao%2C+Y">Yi Qiao</a>, <a href="/search/math-ph?searchtype=author&query=Cao%2C+J">Junpeng Cao</a>, <a href="/search/math-ph?searchtype=author&query=Yang%2C+W">Wen-Li Yang</a>, <a href="/search/math-ph?searchtype=author&query=Shi%2C+K">Kangjie Shi</a>, <a href="/search/math-ph?searchtype=author&query=Wang%2C+Y">Yupeng Wang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2205.10818v2-abstract-short" style="display: inline;"> The exact solution of the $D^{(1)}_2$ quantum spin chain with generic non-diagonal boundary reflections is obtained. It is found that the generating functional of conserved quantities of the system can be factorized as the product of transfer matrices of two anisotropic $XXZ$ spin chains with open boundary conditions. By using the factorization identities and the fusion technique, the eigenvalues… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2205.10818v2-abstract-full').style.display = 'inline'; document.getElementById('2205.10818v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2205.10818v2-abstract-full" style="display: none;"> The exact solution of the $D^{(1)}_2$ quantum spin chain with generic non-diagonal boundary reflections is obtained. It is found that the generating functional of conserved quantities of the system can be factorized as the product of transfer matrices of two anisotropic $XXZ$ spin chains with open boundary conditions. By using the factorization identities and the fusion technique, the eigenvalues and the Bethe ansatz equations of the model are obtained. The eigenvalues are also parameterized by the zero roots of the transfer matrix, and the patterns of root distributions are obtained. Based on them, ground states energy and the surface energies induced by the twisted boundary magnetic fields in the thermodynamic limit are obtained. These results are checked by the numerical calculations. The corresponding isotropic limit is also discussed. The results given in this paper are the foundation to study the exact physical properties of high rank $D^{(1)}_{n}$ model by using the nested processes. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2205.10818v2-abstract-full').style.display = 'none'; document.getElementById('2205.10818v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 6 September, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 22 May, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">35 pages, 3 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Nuclear Physics B 984, (2022) 115946 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2202.06531">arXiv:2202.06531</a> <span> [<a href="https://arxiv.org/pdf/2202.06531">pdf</a>, <a href="https://arxiv.org/ps/2202.06531">ps</a>, <a href="https://arxiv.org/format/2202.06531">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Strongly Correlated Electrons">cond-mat.str-el</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Exactly Solvable and Integrable Systems">nlin.SI</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/JHEP04(2022)101">10.1007/JHEP04(2022)101 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Spectrum of the quantum integrable $D^{(2)}_2$ spin chain with generic boundary fields </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Li%2C+G">Guang-Liang Li</a>, <a href="/search/math-ph?searchtype=author&query=Cao%2C+J">Junpeng Cao</a>, <a href="/search/math-ph?searchtype=author&query=Yang%2C+W">Wen-Li Yang</a>, <a href="/search/math-ph?searchtype=author&query=Shi%2C+K">Kangjie Shi</a>, <a href="/search/math-ph?searchtype=author&query=Wang%2C+Y">Yupeng Wang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2202.06531v2-abstract-short" style="display: inline;"> Exact solution of the quantum integrable $D^{(2)}_2$ spin chain with generic integrable boundary fields is constructed. It is found that the transfer matrix of this model can be factorized as the product of those of two open staggered anisotropic XXZ spin chains. Based on this identity, the eigenvalues and Bethe ansatz equations of the $D^{(2)}_2$ model are derived via off-diagonal Bethe ansatz. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2202.06531v2-abstract-full" style="display: none;"> Exact solution of the quantum integrable $D^{(2)}_2$ spin chain with generic integrable boundary fields is constructed. It is found that the transfer matrix of this model can be factorized as the product of those of two open staggered anisotropic XXZ spin chains. Based on this identity, the eigenvalues and Bethe ansatz equations of the $D^{(2)}_2$ model are derived via off-diagonal Bethe ansatz. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2202.06531v2-abstract-full').style.display = 'none'; document.getElementById('2202.06531v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 April, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 14 February, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">20 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> JHEP 04 (2022) 101 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2201.00963">arXiv:2201.00963</a> <span> [<a href="https://arxiv.org/pdf/2201.00963">pdf</a>, <a href="https://arxiv.org/ps/2201.00963">ps</a>, <a href="https://arxiv.org/format/2201.00963">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Exactly Solvable and Integrable Systems">nlin.SI</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/s00220-022-04566-9">10.1007/s00220-022-04566-9 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Spectrum of the transfer matrices of the spin chains associated with the $A^{(2)}_3$ Lie algebra </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Li%2C+G">Guang-Liang Li</a>, <a href="/search/math-ph?searchtype=author&query=Cao%2C+J">Junpeng Cao</a>, <a href="/search/math-ph?searchtype=author&query=Xu%2C+X">Xiao-Tian Xu</a>, <a href="/search/math-ph?searchtype=author&query=Hao%2C+K">Kun Hao</a>, <a href="/search/math-ph?searchtype=author&query=Sun%2C+P">Pei Sun</a>, <a href="/search/math-ph?searchtype=author&query=Yang%2C+T">Tao Yang</a>, <a href="/search/math-ph?searchtype=author&query=Yang%2C+W">Wen-Li Yang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2201.00963v2-abstract-short" style="display: inline;"> We study the exact solution of quantum integrable system associated with the $A^{(2)}_3$ twist Lie algebra, where the boundary reflection matrices have non-diagonal elements thus the $U(1)$ symmetry is broken. With the help of the fusion technique, we obtain the closed recursive relations of the fused transfer matrices. Based on them, together with the asymptotic behaviors and the values at specia… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2201.00963v2-abstract-full').style.display = 'inline'; document.getElementById('2201.00963v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2201.00963v2-abstract-full" style="display: none;"> We study the exact solution of quantum integrable system associated with the $A^{(2)}_3$ twist Lie algebra, where the boundary reflection matrices have non-diagonal elements thus the $U(1)$ symmetry is broken. With the help of the fusion technique, we obtain the closed recursive relations of the fused transfer matrices. Based on them, together with the asymptotic behaviors and the values at special points, we obtain the eigenvalues and Bethe ansatz equations of the system. We also show that the method is universal and valid for the periodic boundary condition where the $U(1)$ symmetry is reserved. The results in this paper can be applied to studying the exact solution of the $A^{(2)}_n$-related integrable models with arbitrary $n$. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2201.00963v2-abstract-full').style.display = 'none'; document.getElementById('2201.00963v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 19 April, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 3 January, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">26 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Commun. Math. Phys. 399, 651-672 (2023) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2110.05907">arXiv:2110.05907</a> <span> [<a href="https://arxiv.org/pdf/2110.05907">pdf</a>, <a href="https://arxiv.org/ps/2110.05907">ps</a>, <a href="https://arxiv.org/format/2110.05907">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Analysis of PDEs">math.AP</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> </div> <p class="title is-5 mathjax"> Long time asymptotic behavior for the nonlocal nonlinear Schr枚dinger equation with weighted Sobolev initial data </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Li%2C+G">Gaozhan Li</a>, <a href="/search/math-ph?searchtype=author&query=Yang%2C+Y">Yiling Yang</a>, <a href="/search/math-ph?searchtype=author&query=Fan%2C+E">Engui Fan</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2110.05907v2-abstract-short" style="display: inline;"> In this paper, we extend $\overline\partial$ steepest descent method to study the Cauchy problem for the nonlocal nonlinear Schr枚dinger (NNLS) equation with weighted Sobolev initial data %and finite density initial data \begin{align*} &iq_{t}+q_{xx}+2蟽q^2(x,t)\overline{q}(-x,t)=0, & q(x,0)=q_0(x), \end{align*} where $ q_0(x)\in L^{1,1}(\mathbb{R})\cap L^{2,1/2}(\mathbb{R})$. Based on the spect… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2110.05907v2-abstract-full').style.display = 'inline'; document.getElementById('2110.05907v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2110.05907v2-abstract-full" style="display: none;"> In this paper, we extend $\overline\partial$ steepest descent method to study the Cauchy problem for the nonlocal nonlinear Schr枚dinger (NNLS) equation with weighted Sobolev initial data %and finite density initial data \begin{align*} &iq_{t}+q_{xx}+2蟽q^2(x,t)\overline{q}(-x,t)=0, & q(x,0)=q_0(x), \end{align*} where $ q_0(x)\in L^{1,1}(\mathbb{R})\cap L^{2,1/2}(\mathbb{R})$. Based on the spectral analysis of the Lax pair, the solution of the Cauchy problem is expressed in terms of solutions of a Riemann-Hilbert problem, which is transformed into a solvable model after a series of deformations. Finally, we obtain the asymptotic expansion of the Cauchy problem for the NNLS equation in solitonic region. The leading order term is soliton solutions, the second term is the error term is the interaction between solitons and dispersion, the error term comes from the corresponding $\bar{\partial}$ equation. Compared to the asymptotic results on the classical NLS equation, the major difference is the second and third terms in asymptotic expansion for the NNLS equation were affected by a function $ {\rm Im}谓(尉)$ for the stationary phase point $尉$. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2110.05907v2-abstract-full').style.display = 'none'; document.getElementById('2110.05907v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 26 November, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 12 October, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">20 pages. The article has been accepted for publication in SCIENCE CHINA Mathematics</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2110.02699">arXiv:2110.02699</a> <span> [<a href="https://arxiv.org/pdf/2110.02699">pdf</a>, <a href="https://arxiv.org/ps/2110.02699">ps</a>, <a href="https://arxiv.org/format/2110.02699">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/JHEP03(2022)175">10.1007/JHEP03(2022)175 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Exact solution of the quantum integrable model associated with the twisted $D^{(2)}_3$ algebra </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Li%2C+G">Guang-Liang Li</a>, <a href="/search/math-ph?searchtype=author&query=Xu%2C+X">Xiaotian Xu</a>, <a href="/search/math-ph?searchtype=author&query=Hao%2C+K">Kun Hao</a>, <a href="/search/math-ph?searchtype=author&query=Sun%2C+P">Pei Sun</a>, <a href="/search/math-ph?searchtype=author&query=Cao%2C+J">Junpeng Cao</a>, <a href="/search/math-ph?searchtype=author&query=Yang%2C+W">Wen-Li Yang</a>, <a href="/search/math-ph?searchtype=author&query=Shi%2C+K">Kangjie Shi</a>, <a href="/search/math-ph?searchtype=author&query=Wang%2C+Y">Yupeng Wang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2110.02699v2-abstract-short" style="display: inline;"> We generalize the nested off-diagonal Bethe ansatz method to study the quantum chain associated with the twisted $D^{(2)}_3$ algebra (or the $D^{(2)}_3$ model) with either periodic or integrable open boundary conditions. We obtain the intrinsic operator product identities among the fused transfer matrices and find a way to close the recursive fusion relations, which makes it possible to determinat… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2110.02699v2-abstract-full').style.display = 'inline'; document.getElementById('2110.02699v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2110.02699v2-abstract-full" style="display: none;"> We generalize the nested off-diagonal Bethe ansatz method to study the quantum chain associated with the twisted $D^{(2)}_3$ algebra (or the $D^{(2)}_3$ model) with either periodic or integrable open boundary conditions. We obtain the intrinsic operator product identities among the fused transfer matrices and find a way to close the recursive fusion relations, which makes it possible to determinate eigenvalues of transfer matrices with an arbitrary anisotropic parameter $畏$. Based on them, and the asymptotic behaviors and values at certain points, we construct eigenvalues of transfer matrices in terms of homogeneous $T-Q$ relations for the periodic case and inhomogeneous ones for the open case with some off-diagonal boundary reflections. The associated Bethe ansatz equations are also given. The method and results in this paper can be generalized to the $D^{(2)}_{n+1}$ model and other high rank integrable models. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2110.02699v2-abstract-full').style.display = 'none'; document.getElementById('2110.02699v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 25 March, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 6 October, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">40 pages, no figure</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> JHEP03(2022)175 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2011.02746">arXiv:2011.02746</a> <span> [<a href="https://arxiv.org/pdf/2011.02746">pdf</a>, <a href="https://arxiv.org/ps/2011.02746">ps</a>, <a href="https://arxiv.org/format/2011.02746">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.nuclphysb.2021.115333">10.1016/j.nuclphysb.2021.115333 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Exact solutions of the $C_n$ quantum spin chain </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Li%2C+G">Guang-Liang Li</a>, <a href="/search/math-ph?searchtype=author&query=Xue%2C+P">Panpan Xue</a>, <a href="/search/math-ph?searchtype=author&query=Sun%2C+P">Pei Sun</a>, <a href="/search/math-ph?searchtype=author&query=Yang%2C+H">Hulin Yang</a>, <a href="/search/math-ph?searchtype=author&query=Xu%2C+X">Xiaotian Xu</a>, <a href="/search/math-ph?searchtype=author&query=Cao%2C+J">Junpeng Cao</a>, <a href="/search/math-ph?searchtype=author&query=Yang%2C+T">Tao Yang</a>, <a href="/search/math-ph?searchtype=author&query=Yang%2C+W">Wen-Li Yang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2011.02746v2-abstract-short" style="display: inline;"> We study the exact solutions of quantum integrable model associated with the $C_n$ Lie algebra, with either a periodic or an open one with off-diagonal boundary reflections, by generalizing the nested off-diagonal Bethe ansatz method. Taking the $C_3$ as an example we demonstrate how the generalized method works. We give the fusion structures of the model and provide a way to close fusion processe… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2011.02746v2-abstract-full').style.display = 'inline'; document.getElementById('2011.02746v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2011.02746v2-abstract-full" style="display: none;"> We study the exact solutions of quantum integrable model associated with the $C_n$ Lie algebra, with either a periodic or an open one with off-diagonal boundary reflections, by generalizing the nested off-diagonal Bethe ansatz method. Taking the $C_3$ as an example we demonstrate how the generalized method works. We give the fusion structures of the model and provide a way to close fusion processes. Based on the resulted operator product identities among fused transfer matrices and some necessary additional constraints such as asymptotic behaviors and relations at some special points, we obtain the eigenvalues of transfer matrices and parameterize them as homogeneous $T-Q$ relations in the periodic case or inhomogeneous ones in the open case. We also give the exact solutions of the $C_n$ model with an off-diagonal open boundary condition. The method and results in this paper can be generalized to other high rank integrable models associated with other Lie algebras. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2011.02746v2-abstract-full').style.display = 'none'; document.getElementById('2011.02746v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 23 February, 2021; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 5 November, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Nuclear Physics B 965 (2021), 115333 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1909.08534">arXiv:1909.08534</a> <span> [<a href="https://arxiv.org/pdf/1909.08534">pdf</a>, <a href="https://arxiv.org/ps/1909.08534">ps</a>, <a href="https://arxiv.org/format/1909.08534">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/JHEP12(2019)051">10.1007/JHEP12(2019)051 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Off-diagonal Bethe Ansatz for the $D^{(1)}_3$ model </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Li%2C+G">Guang-Liang Li</a>, <a href="/search/math-ph?searchtype=author&query=Cao%2C+J">Junpeng Cao</a>, <a href="/search/math-ph?searchtype=author&query=Xue%2C+P">Panpan Xue</a>, <a href="/search/math-ph?searchtype=author&query=Hao%2C+K">Kun Hao</a>, <a href="/search/math-ph?searchtype=author&query=Sun%2C+P">Pei Sun</a>, <a href="/search/math-ph?searchtype=author&query=Yang%2C+W">Wen-Li Yang</a>, <a href="/search/math-ph?searchtype=author&query=Shi%2C+K">Kangjie Shi</a>, <a href="/search/math-ph?searchtype=author&query=Wang%2C+Y">Yupeng Wang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1909.08534v4-abstract-short" style="display: inline;"> The exact solutions of the $D^{(1)}_3$ model (or the $so(6)$ quantum spin chain) with either periodic or general integrable open boundary conditions are obtained by using the off-diagonal Bethe Ansatz. From the fusion, the complete operator product identities are obtained, which are sufficient to enable us to determine spectrum of the system. Eigenvalues of the fused transfer matrices are construc… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1909.08534v4-abstract-full').style.display = 'inline'; document.getElementById('1909.08534v4-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1909.08534v4-abstract-full" style="display: none;"> The exact solutions of the $D^{(1)}_3$ model (or the $so(6)$ quantum spin chain) with either periodic or general integrable open boundary conditions are obtained by using the off-diagonal Bethe Ansatz. From the fusion, the complete operator product identities are obtained, which are sufficient to enable us to determine spectrum of the system. Eigenvalues of the fused transfer matrices are constructed by the $T-Q$ relations for the periodic case and by the inhomogeneous $T-Q$ one for the non-diagonal boundary reflection case. The present method can be generalized to deal with the $D^{(1)}_{n}$ model directly. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1909.08534v4-abstract-full').style.display = 'none'; document.getElementById('1909.08534v4-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 26 December, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 17 September, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">typos are corrected. arXiv admin note: text overlap with arXiv:1902.08891</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> JHEP 12 (2019) 051 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1902.08891">arXiv:1902.08891</a> <span> [<a href="https://arxiv.org/pdf/1902.08891">pdf</a>, <a href="https://arxiv.org/ps/1902.08891">ps</a>, <a href="https://arxiv.org/format/1902.08891">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.nuclphysb.2019.114719">10.1016/j.nuclphysb.2019.114719 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Off-diagonal Bethe Ansatz on the $so(5)$ spin chain </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Li%2C+G">Guang-Liang Li</a>, <a href="/search/math-ph?searchtype=author&query=Cao%2C+J">Junpeng Cao</a>, <a href="/search/math-ph?searchtype=author&query=Xue%2C+P">Panpan Xue</a>, <a href="/search/math-ph?searchtype=author&query=Hao%2C+K">Kun Hao</a>, <a href="/search/math-ph?searchtype=author&query=Sun%2C+P">Pei Sun</a>, <a href="/search/math-ph?searchtype=author&query=Yang%2C+W">Wen-Li Yang</a>, <a href="/search/math-ph?searchtype=author&query=Shi%2C+K">Kangjie Shi</a>, <a href="/search/math-ph?searchtype=author&query=Wang%2C+Y">Yupeng Wang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1902.08891v2-abstract-short" style="display: inline;"> The $so(5)$ (i.e., $B_2$) quantum integrable spin chains with both periodic and non-diagonal boundaries are studied via the off-diagonal Bethe Ansatz method. By using the fusion technique, sufficient operator product identities (comparing to those in [1]) to determine the spectrum of the transfer matrices are derived. For the periodic case, we recover the results obtained in \cite{NYReshetikhin1},… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1902.08891v2-abstract-full').style.display = 'inline'; document.getElementById('1902.08891v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1902.08891v2-abstract-full" style="display: none;"> The $so(5)$ (i.e., $B_2$) quantum integrable spin chains with both periodic and non-diagonal boundaries are studied via the off-diagonal Bethe Ansatz method. By using the fusion technique, sufficient operator product identities (comparing to those in [1]) to determine the spectrum of the transfer matrices are derived. For the periodic case, we recover the results obtained in \cite{NYReshetikhin1}, while for the non-diagonal boundary case, a new inhomogeneous $T-Q$ relation is constructed. The present method can be directly generalized to deal with the $so(2n+1)$ (i.e., $B_n$) quantum integrable spin chains with general boundaries. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1902.08891v2-abstract-full').style.display = 'none'; document.getElementById('1902.08891v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 17 September, 2019; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 23 February, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Published version, 42 pages, no figure</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Nucl. Phys. B 946, 114719 (2019) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1812.03618">arXiv:1812.03618</a> <span> [<a href="https://arxiv.org/pdf/1812.03618">pdf</a>, <a href="https://arxiv.org/ps/1812.03618">ps</a>, <a href="https://arxiv.org/format/1812.03618">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/JHEP05(2019)067">10.1007/JHEP05(2019)067 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Exact solution of the $sp(4)$ integrable spin chain with generic boundaries </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Li%2C+G">Guang-Liang Li</a>, <a href="/search/math-ph?searchtype=author&query=Cao%2C+J">Junpeng Cao</a>, <a href="/search/math-ph?searchtype=author&query=Xue%2C+P">Panpan Xue</a>, <a href="/search/math-ph?searchtype=author&query=Xin%2C+Z">Zhi-Rong Xin</a>, <a href="/search/math-ph?searchtype=author&query=Hao%2C+K">Kun Hao</a>, <a href="/search/math-ph?searchtype=author&query=Yang%2C+W">Wen-Li Yang</a>, <a href="/search/math-ph?searchtype=author&query=Shi%2C+K">Kangjie Shi</a>, <a href="/search/math-ph?searchtype=author&query=Wang%2C+Y">Yupeng Wang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1812.03618v2-abstract-short" style="display: inline;"> The off-diagonal Bethe ansatz method is generalized to the integrable model associated with the $sp(4)$ (or $C_2$) Lie algebra. By using the fusion technique, we obtain the complete operator product identities among the fused transfer matrices. These relations, together with some asymptotic behaviors and values of the transfer matrices at certain points, enable us to determine the eigenvalues of t… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1812.03618v2-abstract-full').style.display = 'inline'; document.getElementById('1812.03618v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1812.03618v2-abstract-full" style="display: none;"> The off-diagonal Bethe ansatz method is generalized to the integrable model associated with the $sp(4)$ (or $C_2$) Lie algebra. By using the fusion technique, we obtain the complete operator product identities among the fused transfer matrices. These relations, together with some asymptotic behaviors and values of the transfer matrices at certain points, enable us to determine the eigenvalues of the transfer matrices completely. For the periodic boundary condition case, we recover the same $T-Q$ relations obtained via conventional Bethe ansatz methods previously, while for the off-diagonal boundary condition case, the eigenvalues are given in terms of inhomogeneous $T-Q$ relations, which could not be obtained by the conventional Bethe ansatz methods. The method developed in this paper can be directly generalized to generic $sp(2n)$ (i.e., $C_n$) integrable model. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1812.03618v2-abstract-full').style.display = 'none'; document.getElementById('1812.03618v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 16 May, 2019; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 9 December, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Published version, 20 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> JHEP 05 (2019) 067 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1812.02011">arXiv:1812.02011</a> <span> [<a href="https://arxiv.org/pdf/1812.02011">pdf</a>, <a href="https://arxiv.org/format/1812.02011">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Mesoscale and Nanoscale Physics">cond-mat.mes-hall</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Materials Science">cond-mat.mtrl-sci</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Other Condensed Matter">cond-mat.other</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> </div> <p class="title is-5 mathjax"> Tidal surface states as fingerprints of non-Hermitian nodal knot metals </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Zhang%2C+X">Xiao Zhang</a>, <a href="/search/math-ph?searchtype=author&query=Li%2C+G">Guangjie Li</a>, <a href="/search/math-ph?searchtype=author&query=Liu%2C+Y">Yuhan Liu</a>, <a href="/search/math-ph?searchtype=author&query=Tai%2C+T">Tommy Tai</a>, <a href="/search/math-ph?searchtype=author&query=Thomale%2C+R">Ronny Thomale</a>, <a href="/search/math-ph?searchtype=author&query=Lee%2C+C+H">Ching Hua Lee</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1812.02011v4-abstract-short" style="display: inline;"> Non-Hermitian nodal knot metals (NKMs) contains intricate complex-valued energy bands gives rise to knotted exceptional loops and new topological surface states. We introduce a formalism that connects the algebraic, geometric, and topological aspects of these surface states with their parent knots, and provide an optimized constructive ansatz for tight-binding models for non-Hermitian NKMs of arbi… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1812.02011v4-abstract-full').style.display = 'inline'; document.getElementById('1812.02011v4-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1812.02011v4-abstract-full" style="display: none;"> Non-Hermitian nodal knot metals (NKMs) contains intricate complex-valued energy bands gives rise to knotted exceptional loops and new topological surface states. We introduce a formalism that connects the algebraic, geometric, and topological aspects of these surface states with their parent knots, and provide an optimized constructive ansatz for tight-binding models for non-Hermitian NKMs of arbitrary knot complexity and minimal hybridization range. Specifically, various representative non-Hermitian torus knots Hamiltonians are constructed in real-space, and their nodal topologies studied via winding numbers that avoid the explicit construction of generalized Brillouin zones. In particular, we identify the surface state boundaries as "tidal" intersections of the complex band structure in a marine landscape analogy. Beyond topological quantities based on Berry phases, we further find these tidal surface states to be intimately connected to the band vorticity and the layer structure of their dual Seifert surface, and as such provide a fingerprint for non-Hermitian NKMs. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1812.02011v4-abstract-full').style.display = 'none'; document.getElementById('1812.02011v4-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 28 February, 2021; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 3 December, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">22 pages, 18 figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1712.08525">arXiv:1712.08525</a> <span> [<a href="https://arxiv.org/pdf/1712.08525">pdf</a>, <a href="https://arxiv.org/ps/1712.08525">ps</a>, <a href="https://arxiv.org/format/1712.08525">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.nuclphysb.2018.04.025">10.1016/j.nuclphysb.2018.04.025 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Bethe states of the trigonometric SU(3) spin chain with generic open boundaries </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Sun%2C+P">Pei Sun</a>, <a href="/search/math-ph?searchtype=author&query=Xin%2C+Z">Zhirong Xin</a>, <a href="/search/math-ph?searchtype=author&query=Qiao%2C+Y">Yi Qiao</a>, <a href="/search/math-ph?searchtype=author&query=Wen%2C+F">Fakai Wen</a>, <a href="/search/math-ph?searchtype=author&query=Hao%2C+K">Kun Hao</a>, <a href="/search/math-ph?searchtype=author&query=Cao%2C+J">Junpeng Cao</a>, <a href="/search/math-ph?searchtype=author&query=Li%2C+G">Guang-Liang Li</a>, <a href="/search/math-ph?searchtype=author&query=Yang%2C+T">Tao Yang</a>, <a href="/search/math-ph?searchtype=author&query=Yang%2C+W">Wen-Li Yang</a>, <a href="/search/math-ph?searchtype=author&query=Shi%2C+K">Kangjie Shi</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1712.08525v2-abstract-short" style="display: inline;"> By combining the algebraic Bethe ansatz and the off-diagonal Bethe ansatz, we investigate the trigonometric SU(3) model with generic open boundaries. The eigenvalues of the transfer matrix are given in terms of an inhomogeneous T-Q relation, and the corresponding eigenstates are expressed in terms of nested Bethe-type eigenstates which have well-defined homogeneous limit. This exact solution provi… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1712.08525v2-abstract-full').style.display = 'inline'; document.getElementById('1712.08525v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1712.08525v2-abstract-full" style="display: none;"> By combining the algebraic Bethe ansatz and the off-diagonal Bethe ansatz, we investigate the trigonometric SU(3) model with generic open boundaries. The eigenvalues of the transfer matrix are given in terms of an inhomogeneous T-Q relation, and the corresponding eigenstates are expressed in terms of nested Bethe-type eigenstates which have well-defined homogeneous limit. This exact solution provides a basis for further analyzing the thermodynamic properties and correlation functions of the anisotropic models associated with higher rank algebras. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1712.08525v2-abstract-full').style.display = 'none'; document.getElementById('1712.08525v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 24 June, 2018; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 21 December, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2017. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">17 pages, 3 tables. arXiv admin note: text overlap with arXiv:1705.09478</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Nuclear Physics B 931, 342 (2018) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1705.09478">arXiv:1705.09478</a> <span> [<a href="https://arxiv.org/pdf/1705.09478">pdf</a>, <a href="https://arxiv.org/format/1705.09478">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Strongly Correlated Electrons">cond-mat.str-el</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/JHEP07(2017)051">10.1007/JHEP07(2017)051 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> On the Bethe states of the one-dimensional supersymmetric t-J model with generic open boundaries </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Sun%2C+P">Pei Sun</a>, <a href="/search/math-ph?searchtype=author&query=Wen%2C+F">Fakai Wen</a>, <a href="/search/math-ph?searchtype=author&query=Hao%2C+K">Kun Hao</a>, <a href="/search/math-ph?searchtype=author&query=Cao%2C+J">Junpeng Cao</a>, <a href="/search/math-ph?searchtype=author&query=Li%2C+G">Guang-Liang Li</a>, <a href="/search/math-ph?searchtype=author&query=Yang%2C+W">Wen-Li Yang</a>, <a href="/search/math-ph?searchtype=author&query=Shi%2C+K">Kangjie Shi</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1705.09478v3-abstract-short" style="display: inline;"> By combining the algebraic Bethe ansatz and the off-diagonal Bethe ansatz, we investigate the supersymmetric t-J model with generic open boundaries. The eigenvalues of the transfer matrix are given in terms of an inhomogeneous T-Q relation, and the corresponding eigenstates are expressed in terms of nested Bethe states which have well-defined homogeneous limit. This exact solution provides basis f… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1705.09478v3-abstract-full').style.display = 'inline'; document.getElementById('1705.09478v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1705.09478v3-abstract-full" style="display: none;"> By combining the algebraic Bethe ansatz and the off-diagonal Bethe ansatz, we investigate the supersymmetric t-J model with generic open boundaries. The eigenvalues of the transfer matrix are given in terms of an inhomogeneous T-Q relation, and the corresponding eigenstates are expressed in terms of nested Bethe states which have well-defined homogeneous limit. This exact solution provides basis for further analyzing the thermodynamic properties and correlation functions of the model. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1705.09478v3-abstract-full').style.display = 'none'; document.getElementById('1705.09478v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 12 July, 2017; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 26 May, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2017. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">17 pages, 2 tables, published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> JHEP07(2017)051 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1705.08114">arXiv:1705.08114</a> <span> [<a href="https://arxiv.org/pdf/1705.08114">pdf</a>, <a href="https://arxiv.org/ps/1705.08114">ps</a>, <a href="https://arxiv.org/format/1705.08114">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Exactly Solvable and Integrable Systems">nlin.SI</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.nuclphysb.2018.03.010">10.1016/j.nuclphysb.2018.03.010 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> A convenient basis for the Izergin-Korepin model </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Qiao%2C+Y">Yi Qiao</a>, <a href="/search/math-ph?searchtype=author&query=Zhang%2C+X">Xin Zhang</a>, <a href="/search/math-ph?searchtype=author&query=Hao%2C+K">Kun Hao</a>, <a href="/search/math-ph?searchtype=author&query=Cao%2C+J">Junpeng Cao</a>, <a href="/search/math-ph?searchtype=author&query=Li%2C+G">Guang-Liang Li</a>, <a href="/search/math-ph?searchtype=author&query=Yang%2C+W">Wen-Li Yang</a>, <a href="/search/math-ph?searchtype=author&query=Shi%2C+K">Kangjie Shi</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1705.08114v2-abstract-short" style="display: inline;"> We propose a convenient orthogonal basis of the Hilbert space for the Izergin-Korepin model (or the quantum spin chain associated with the $A^{(2)}_{2}$ algebra). It is shown that the monodromy-matrix elements acting on the basis take relatively simple forms (c.f. acting on the original basis ), which is quite similar as that in the so-called F-basis for the quantum spin chains associated with… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1705.08114v2-abstract-full').style.display = 'inline'; document.getElementById('1705.08114v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1705.08114v2-abstract-full" style="display: none;"> We propose a convenient orthogonal basis of the Hilbert space for the Izergin-Korepin model (or the quantum spin chain associated with the $A^{(2)}_{2}$ algebra). It is shown that the monodromy-matrix elements acting on the basis take relatively simple forms (c.f. acting on the original basis ), which is quite similar as that in the so-called F-basis for the quantum spin chains associated with $A$-type (super)algebras. As an application, we present the recursive expressions of Bethe states in the basis for the Izergin-Korepin model. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1705.08114v2-abstract-full').style.display = 'none'; document.getElementById('1705.08114v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 3 April, 2018; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 23 May, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2017. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">24 pages, no figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Nucl.Phys.B 930: 399-417 2018 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1609.00953">arXiv:1609.00953</a> <span> [<a href="https://arxiv.org/pdf/1609.00953">pdf</a>, <a href="https://arxiv.org/ps/1609.00953">ps</a>, <a href="https://arxiv.org/format/1609.00953">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.nuclphysb.2017.04.019">10.1016/j.nuclphysb.2017.04.019 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> On the solutions of the $Z_n$-Belavin model with arbitrary number of sites </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Hao%2C+K">Kun Hao</a>, <a href="/search/math-ph?searchtype=author&query=Cao%2C+J">Junpeng Cao</a>, <a href="/search/math-ph?searchtype=author&query=Li%2C+G">Guang-Liang Li</a>, <a href="/search/math-ph?searchtype=author&query=Yang%2C+W">Wen-Li Yang</a>, <a href="/search/math-ph?searchtype=author&query=Shi%2C+K">Kangjie Shi</a>, <a href="/search/math-ph?searchtype=author&query=Wang%2C+Y">Yupeng Wang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1609.00953v2-abstract-short" style="display: inline;"> The periodic $Z_n$-Belavin model on a lattice with an arbitrary number of sites $N$ is studied via the off-diagonal Bethe Ansatz method (ODBA). The eigenvalues of the corresponding transfer matrix are given in terms of an unified inhomogeneous $T-Q$ relation. In the special case of $N=nl$ with $l$ being also a positive integer, the resulting $T-Q$ relation recovers the homogeneous one previously o… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1609.00953v2-abstract-full').style.display = 'inline'; document.getElementById('1609.00953v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1609.00953v2-abstract-full" style="display: none;"> The periodic $Z_n$-Belavin model on a lattice with an arbitrary number of sites $N$ is studied via the off-diagonal Bethe Ansatz method (ODBA). The eigenvalues of the corresponding transfer matrix are given in terms of an unified inhomogeneous $T-Q$ relation. In the special case of $N=nl$ with $l$ being also a positive integer, the resulting $T-Q$ relation recovers the homogeneous one previously obtained via algebraic Bethe Ansatz. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1609.00953v2-abstract-full').style.display = 'none'; document.getElementById('1609.00953v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 24 May, 2017; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 4 September, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2016. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">24pages, no figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Nuclear Physics B 920 (2017) 419-441 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1602.02042">arXiv:1602.02042</a> <span> [<a href="https://arxiv.org/pdf/1602.02042">pdf</a>, <a href="https://arxiv.org/ps/1602.02042">ps</a>, <a href="https://arxiv.org/format/1602.02042">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.nuclphysb.2016.07.011">10.1016/j.nuclphysb.2016.07.011 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Exact solution of the trigonometric SU(3) spin chain with generic off-diagonal boundary reflections </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Li%2C+G">Guang-Liang Li</a>, <a href="/search/math-ph?searchtype=author&query=Cao%2C+J">Junpeng Cao</a>, <a href="/search/math-ph?searchtype=author&query=Hao%2C+K">Kun Hao</a>, <a href="/search/math-ph?searchtype=author&query=Wen%2C+F">Fakai Wen</a>, <a href="/search/math-ph?searchtype=author&query=Yang%2C+W">Wen-Li Yang</a>, <a href="/search/math-ph?searchtype=author&query=Shi%2C+K">Kangjie Shi</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1602.02042v3-abstract-short" style="display: inline;"> The nested off-diagonal Bethe ansatz is generalized to study the quantum spin chain associated with the $SU_q(3)$ R-matrix and generic integrable non-diagonal boundary conditions. By using the fusion technique, certain closed operator identities among the fused transfer matrices at the inhomogeneous points are derived. The corresponding asymptotic behaviors of the transfer matrices and their value… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1602.02042v3-abstract-full').style.display = 'inline'; document.getElementById('1602.02042v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1602.02042v3-abstract-full" style="display: none;"> The nested off-diagonal Bethe ansatz is generalized to study the quantum spin chain associated with the $SU_q(3)$ R-matrix and generic integrable non-diagonal boundary conditions. By using the fusion technique, certain closed operator identities among the fused transfer matrices at the inhomogeneous points are derived. The corresponding asymptotic behaviors of the transfer matrices and their values at some special points are given in detail. Based on the functional analysis, a nested inhomogeneous T-Q relations and Bethe ansatz equations of the system are obtained. These results can be naturally generalized to cases related to the $SU_q(n)$ algebra. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1602.02042v3-abstract-full').style.display = 'none'; document.getElementById('1602.02042v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 17 August, 2016; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 5 February, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2016. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">published version, 27 pages, 1 table, 1 figure</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Nucl. Phys. B 910 (2016), 410-430 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1601.04771">arXiv:1601.04771</a> <span> [<a href="https://arxiv.org/pdf/1601.04771">pdf</a>, <a href="https://arxiv.org/ps/1601.04771">ps</a>, <a href="https://arxiv.org/format/1601.04771">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/JHEP05(2016)119">10.1007/JHEP05(2016)119 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> A representation basis for the quantum integrable spin chain associated with the su(3) algebra </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Hao%2C+K">Kun Hao</a>, <a href="/search/math-ph?searchtype=author&query=Cao%2C+J">Junpeng Cao</a>, <a href="/search/math-ph?searchtype=author&query=Li%2C+G">Guang-Liang Li</a>, <a href="/search/math-ph?searchtype=author&query=Yang%2C+W">Wen-Li Yang</a>, <a href="/search/math-ph?searchtype=author&query=Shi%2C+K">Kangjie Shi</a>, <a href="/search/math-ph?searchtype=author&query=Wang%2C+Y">Yupeng Wang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1601.04771v3-abstract-short" style="display: inline;"> An orthogonal basis of the Hilbert space for the quantum spin chain associated with the su(3) algebra is introduced. Such kind of basis could be treated as a nested generalization of separation of variables (SoV) basis for high-rank quantum integrable models. It is found that all the monodromy-matrix elements acting on a basis vector take simple forms. With the help of the basis, we construct eige… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1601.04771v3-abstract-full').style.display = 'inline'; document.getElementById('1601.04771v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1601.04771v3-abstract-full" style="display: none;"> An orthogonal basis of the Hilbert space for the quantum spin chain associated with the su(3) algebra is introduced. Such kind of basis could be treated as a nested generalization of separation of variables (SoV) basis for high-rank quantum integrable models. It is found that all the monodromy-matrix elements acting on a basis vector take simple forms. With the help of the basis, we construct eigenstates of the su(3) inhomogeneous spin torus (the trigonometric su(3) spin chain with antiperiodic boundary condition) from its spectrum obtained via the off-diagonal Bethe Ansatz (ODBA). Based on small sites (i.e. N=2) check, it is conjectured that the homogeneous limit of the eigenstates exists, which gives rise to the corresponding eigenstates of the homogenous model. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1601.04771v3-abstract-full').style.display = 'none'; document.getElementById('1601.04771v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 17 August, 2016; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 18 January, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2016. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">24 pages, no figure, published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> JHEP 05 (2016) 119 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1601.04389">arXiv:1601.04389</a> <span> [<a href="https://arxiv.org/pdf/1601.04389">pdf</a>, <a href="https://arxiv.org/ps/1601.04389">ps</a>, <a href="https://arxiv.org/format/1601.04389">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1088/1742-5468/2016/07/073104">10.1088/1742-5468/2016/07/073104 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Exact solution of an su(n) spin torus </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Hao%2C+K">Kun Hao</a>, <a href="/search/math-ph?searchtype=author&query=Cao%2C+J">Junpeng Cao</a>, <a href="/search/math-ph?searchtype=author&query=Li%2C+G">Guang-Liang Li</a>, <a href="/search/math-ph?searchtype=author&query=Yang%2C+W">Wen-Li Yang</a>, <a href="/search/math-ph?searchtype=author&query=Shi%2C+K">Kangjie Shi</a>, <a href="/search/math-ph?searchtype=author&query=Wang%2C+Y">Yupeng Wang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1601.04389v3-abstract-short" style="display: inline;"> The trigonometric su(n) spin chain with anti-periodic boundary condition (su(n) spin torus) is demonstrated to be Yang-Baxter integrable. Based on some intrinsic properties of the R-matrix, certain operator product identities of the transfer matrix are derived. These identities and the asymptotic behavior of the transfer matrix together allow us to obtain the exact eigenvalues in terms of an inhom… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1601.04389v3-abstract-full').style.display = 'inline'; document.getElementById('1601.04389v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1601.04389v3-abstract-full" style="display: none;"> The trigonometric su(n) spin chain with anti-periodic boundary condition (su(n) spin torus) is demonstrated to be Yang-Baxter integrable. Based on some intrinsic properties of the R-matrix, certain operator product identities of the transfer matrix are derived. These identities and the asymptotic behavior of the transfer matrix together allow us to obtain the exact eigenvalues in terms of an inhomogeneous T-Q relation via the off-diagonal Bethe Ansatz. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1601.04389v3-abstract-full').style.display = 'none'; document.getElementById('1601.04389v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 17 August, 2016; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 17 January, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2016. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">24 pages, no figure, published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J. Stat. Mech. (2016) 073104 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1505.07060">arXiv:1505.07060</a> <span> [<a href="https://arxiv.org/pdf/1505.07060">pdf</a>, <a href="https://arxiv.org/ps/1505.07060">ps</a>, <a href="https://arxiv.org/format/1505.07060">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Analysis of PDEs">math.AP</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> </div> <p class="title is-5 mathjax"> General decay for a viscoelastic wave equation with dynamic boundary conditions and a time-varying delay </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Li%2C+G">Gang Li</a>, <a href="/search/math-ph?searchtype=author&query=Zhu%2C+B">Biqing Zhu</a>, <a href="/search/math-ph?searchtype=author&query=Wang%2C+D">Danhua Wang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1505.07060v6-abstract-short" style="display: inline;"> The goal of this paper is to study a nonlinear viscoelastic wave equation with strong damping, time-varying delay and dynamical boundary condition. By introducing suitable energy and Lyapunov functionals, under suitable assumptions, we then prove a general decay result of the energy, from which the usual exponential and polynomial decay rates are only special cases. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1505.07060v6-abstract-full" style="display: none;"> The goal of this paper is to study a nonlinear viscoelastic wave equation with strong damping, time-varying delay and dynamical boundary condition. By introducing suitable energy and Lyapunov functionals, under suitable assumptions, we then prove a general decay result of the energy, from which the usual exponential and polynomial decay rates are only special cases. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1505.07060v6-abstract-full').style.display = 'none'; document.getElementById('1505.07060v6-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 10 June, 2015; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 25 May, 2015; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2015. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1505.02220">arXiv:1505.02220</a> <span> [<a href="https://arxiv.org/pdf/1505.02220">pdf</a>, <a href="https://arxiv.org/ps/1505.02220">ps</a>, <a href="https://arxiv.org/format/1505.02220">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Analysis of PDEs">math.AP</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> </div> <p class="title is-5 mathjax"> Existence, general decay and blow-up of solutions for a viscoelastic Kirchhoff equation with Balakrishnan-Taylor damping and dynamic boundary conditions </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Li%2C+G">Gang Li</a>, <a href="/search/math-ph?searchtype=author&query=Zhu%2C+B">Biqing Zhu</a>, <a href="/search/math-ph?searchtype=author&query=Wang%2C+D">Danhua Wang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1505.02220v3-abstract-short" style="display: inline;"> Our aim in this article is to study a nonlinear viscoelastic Kirchhoff equation with strong damping, Balakrishnan-Taylor damping, nonlinear source and dynamical boundary condition. Firstly, we prove the local existence of solutions by using the Faedo-Galerkin approximation method combined with a contraction mapping theorem. We then prove that if the initial data enter into the stable set, the solu… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1505.02220v3-abstract-full').style.display = 'inline'; document.getElementById('1505.02220v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1505.02220v3-abstract-full" style="display: none;"> Our aim in this article is to study a nonlinear viscoelastic Kirchhoff equation with strong damping, Balakrishnan-Taylor damping, nonlinear source and dynamical boundary condition. Firstly, we prove the local existence of solutions by using the Faedo-Galerkin approximation method combined with a contraction mapping theorem. We then prove that if the initial data enter into the stable set, the solution globally exists, and if the initial data enter into the unstable set, the solution blows up in a finite time. Moreover, we obtain a general decay result of the energy, from which the usual exponential and polynomial decay rates are only special cases. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1505.02220v3-abstract-full').style.display = 'none'; document.getElementById('1505.02220v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 June, 2015; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 8 May, 2015; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2015. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1403.7915">arXiv:1403.7915</a> <span> [<a href="https://arxiv.org/pdf/1403.7915">pdf</a>, <a href="https://arxiv.org/ps/1403.7915">ps</a>, <a href="https://arxiv.org/format/1403.7915">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/JHEP06(2014)128">10.1007/JHEP06(2014)128 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Exact solution of the Izergin-Korepin model with general non-diagonal boundary terms </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Hao%2C+K">Kun Hao</a>, <a href="/search/math-ph?searchtype=author&query=Cao%2C+J">Junpeng Cao</a>, <a href="/search/math-ph?searchtype=author&query=Li%2C+G">Guang-Liang Li</a>, <a href="/search/math-ph?searchtype=author&query=Yang%2C+W">Wen-Li Yang</a>, <a href="/search/math-ph?searchtype=author&query=Shi%2C+K">Kangjie Shi</a>, <a href="/search/math-ph?searchtype=author&query=Wang%2C+Y">Yupeng Wang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1403.7915v2-abstract-short" style="display: inline;"> The Izergin-Korepin model with general non-diagonal boundary terms, a typical integrable model beyond A-type and without U(1)-symmetry, is studied via the off-diagonal Bethe ansatz method. Based on some intrinsic properties of the R-matrix and the K-matrices, certain operator product identities of the transfer matrix are obtained at some special points of the spectral parameter. These identities a… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1403.7915v2-abstract-full').style.display = 'inline'; document.getElementById('1403.7915v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1403.7915v2-abstract-full" style="display: none;"> The Izergin-Korepin model with general non-diagonal boundary terms, a typical integrable model beyond A-type and without U(1)-symmetry, is studied via the off-diagonal Bethe ansatz method. Based on some intrinsic properties of the R-matrix and the K-matrices, certain operator product identities of the transfer matrix are obtained at some special points of the spectral parameter. These identities and the asymptotic behaviors of the transfer matrix together allow us to construct the inhomogeneous T-Q relation and the associated Bethe ansatz equations. In the diagonal boundary limit, the reduced results coincide exactly with those obtained via other methods. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1403.7915v2-abstract-full').style.display = 'none'; document.getElementById('1403.7915v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 18 July, 2014; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 31 March, 2014; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2014. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">24 pages, published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> JHEP 06 (2014) 128 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/hep-th/0611127">arXiv:hep-th/0611127</a> <span> [<a href="https://arxiv.org/pdf/hep-th/0611127">pdf</a>, <a href="https://arxiv.org/ps/hep-th/0611127">ps</a>, <a href="https://arxiv.org/format/hep-th/0611127">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1088/1742-5468/2007/01/P01018">10.1088/1742-5468/2007/01/P01018 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The algebraic Bethe ansatz for open vertex models </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math-ph?searchtype=author&query=Li%2C+G">Guang-Liang Li</a>, <a href="/search/math-ph?searchtype=author&query=Shi%2C+K">Kang-Jie Shi</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="hep-th/0611127v2-abstract-short" style="display: inline;"> We present a unified algebraic Bethe ansatz for open vertex models which are associated with the non-exceptional $A^{(2)}_{2n},A^{(2)}_{2n-1},B^{(1)}_n,C^{(1)}_n,D^{(1)}_{n}$ Lie algebras. By the method, we solve these models with the trivial K matrix and find that our results agree with that obtained by analytical Bethe ansatz. We also solve the $B^{(1)}_n,C^{(1)}_n,D^{(1)}_{n}$ models with… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('hep-th/0611127v2-abstract-full').style.display = 'inline'; document.getElementById('hep-th/0611127v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="hep-th/0611127v2-abstract-full" style="display: none;"> We present a unified algebraic Bethe ansatz for open vertex models which are associated with the non-exceptional $A^{(2)}_{2n},A^{(2)}_{2n-1},B^{(1)}_n,C^{(1)}_n,D^{(1)}_{n}$ Lie algebras. By the method, we solve these models with the trivial K matrix and find that our results agree with that obtained by analytical Bethe ansatz. We also solve the $B^{(1)}_n,C^{(1)}_n,D^{(1)}_{n}$ models with some non-trivial diagonal K-matrices (one free parameter case) by the algebraic Bethe ansatz. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('hep-th/0611127v2-abstract-full').style.display = 'none'; document.getElementById('hep-th/0611127v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 29 December, 2006; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 11 November, 2006; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2006. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Latex, 35 pages, new content and references are added, minor revisions are made</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J.Stat.Mech.0701:P01018,2007 </p> </li> </ol> <div class="is-hidden-tablet">  <span class="help" style="display: inline-block;"><a href="https://github.com/arXiv/arxiv-search/releases">Search v0.5.6 released 2020-02-24</a>  </span> </div> </div> </main> <footer> <div class="columns is-desktop" role="navigation" aria-label="Secondary">  <div class="column"> <div class="columns"> <div class="column"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/about">About</a></li> <li><a href="https://info.arxiv.org/help">Help</a></li> </ul> </div> <div class="column"> <ul class="nav-spaced"> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>contact arXiv</title><desc>Click here to contact arXiv</desc><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"/></svg> <a href="https://info.arxiv.org/help/contact.html"> Contact</a> </li> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>subscribe to arXiv mailings</title><desc>Click here to subscribe</desc><path d="M476 3.2L12.5 270.6c-18.1 10.4-15.8 35.6 2.2 43.2L121 358.4l287.3-253.2c5.5-4.9 13.3 2.6 8.6 8.3L176 407v80.5c0 23.6 28.5 32.9 42.5 15.8L282 426l124.6 52.2c14.2 6 30.4-2.9 33-18.2l72-432C515 7.8 493.3-6.8 476 3.2z"/></svg> <a href="https://info.arxiv.org/help/subscribe"> Subscribe</a> </li> </ul> </div> </div> </div>   <div class="column"> <div class="columns"> <div class="column"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/help/license/index.html">Copyright</a></li> <li><a href="https://info.arxiv.org/help/policies/privacy_policy.html">Privacy Policy</a></li> </ul> </div> <div class="column sorry-app-links"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/help/web_accessibility.html">Web Accessibility Assistance</a></li> <li> <p class="help"> <a class="a11y-main-link" href="https://status.arxiv.org" target="_blank">arXiv Operational Status <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 256 512" class="icon filter-dark_grey" role="presentation"><path d="M224.3 273l-136 136c-9.4 9.4-24.6 9.4-33.9 0l-22.6-22.6c-9.4-9.4-9.4-24.6 0-33.9l96.4-96.4-96.4-96.4c-9.4-9.4-9.4-24.6 0-33.9L54.3 103c9.4-9.4 24.6-9.4 33.9 0l136 136c9.5 9.4 9.5 24.6.1 34z"/></svg></a><br> Get status notifications via <a class="is-link" href="https://subscribe.sorryapp.com/24846f03/email/new" target="_blank"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"/></svg>email</a> or <a class="is-link" href="https://subscribe.sorryapp.com/24846f03/slack/new" target="_blank"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 448 512" class="icon filter-black" role="presentation"><path d="M94.12 315.1c0 25.9-21.16 47.06-47.06 47.06S0 341 0 315.1c0-25.9 21.16-47.06 47.06-47.06h47.06v47.06zm23.72 0c0-25.9 21.16-47.06 47.06-47.06s47.06 21.16 47.06 47.06v117.84c0 25.9-21.16 47.06-47.06 47.06s-47.06-21.16-47.06-47.06V315.1zm47.06-188.98c-25.9 0-47.06-21.16-47.06-47.06S139 32 164.9 32s47.06 21.16 47.06 47.06v47.06H164.9zm0 23.72c25.9 0 47.06 21.16 47.06 47.06s-21.16 47.06-47.06 47.06H47.06C21.16 243.96 0 222.8 0 196.9s21.16-47.06 47.06-47.06H164.9zm188.98 47.06c0-25.9 21.16-47.06 47.06-47.06 25.9 0 47.06 21.16 47.06 47.06s-21.16 47.06-47.06 47.06h-47.06V196.9zm-23.72 0c0 25.9-21.16 47.06-47.06 47.06-25.9 0-47.06-21.16-47.06-47.06V79.06c0-25.9 21.16-47.06 47.06-47.06 25.9 0 47.06 21.16 47.06 47.06V196.9zM283.1 385.88c25.9 0 47.06 21.16 47.06 47.06 0 25.9-21.16 47.06-47.06 47.06-25.9 0-47.06-21.16-47.06-47.06v-47.06h47.06zm0-23.72c-25.9 0-47.06-21.16-47.06-47.06 0-25.9 21.16-47.06 47.06-47.06h117.84c25.9 0 47.06 21.16 47.06 47.06 0 25.9-21.16 47.06-47.06 47.06H283.1z"/></svg>slack</a> </p> </li> </ul> </div> </div> </div>  </div> </footer> <script src="https://static.arxiv.org/static/base/1.0.0a5/js/member_acknowledgement.js"></script> </body> </html>

CINXE.COM

Search | arXiv e-print repository