CINXE.COM
solid state physics in nLab
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1 plus MathML 2.0 plus SVG 1.1//EN" "http://www.w3.org/2002/04/xhtml-math-svg/xhtml-math-svg-flat.dtd" > <html xmlns="http://www.w3.org/1999/xhtml"> <head> <title> solid state physics in nLab </title> <meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /> <meta name="robots" content="index,follow" /> <meta name="viewport" content="width=device-width, initial-scale=1" /> <link href="/stylesheets/instiki.css?1676280126" media="all" rel="stylesheet" type="text/css" /> <link href="/stylesheets/mathematics.css?1660229990" media="all" rel="stylesheet" type="text/css" /> <link href="/stylesheets/syntax.css?1660229990" media="all" rel="stylesheet" type="text/css" /> <link href="/stylesheets/nlab.css?1676280126" media="all" rel="stylesheet" type="text/css" /> <link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/gh/dreampulse/computer-modern-web-font@master/fonts.css"/> <style type="text/css"> h1#pageName, div.info, .newWikiWord a, a.existingWikiWord, .newWikiWord a:hover, [actiontype="toggle"]:hover, #TextileHelp h3 { color: #226622; } a:visited.existingWikiWord { color: #164416; } </style> <style type="text/css"><!--/*--><![CDATA[/*><!--*/ .toc ul {margin: 0; padding: 0;} .toc ul ul {margin: 0; padding: 0 0 0 10px;} .toc li > p {margin: 0} .toc ul li {list-style-type: none; position: relative;} .toc div {border-top:1px dotted #ccc;} .rightHandSide h2 {font-size: 1.5em;color:#008B26} table.plaintable { border-collapse:collapse; margin-left:30px; border:0; } .plaintable td {border:1px solid #000; padding: 3px;} .plaintable th {padding: 3px;} .plaintable caption { font-weight: bold; font-size:1.1em; text-align:center; margin-left:30px; } /* Query boxes for questioning and answering mechanism */ div.query{ background: #f6fff3; border: solid #ce9; border-width: 2px 1px; padding: 0 1em; margin: 0 1em; max-height: 20em; overflow: auto; } /* Standout boxes for putting important text */ div.standout{ background: #fff1f1; border: solid black; border-width: 2px 1px; padding: 0 1em; margin: 0 1em; overflow: auto; } /* Icon for links to n-category arXiv documents (commented out for now i.e. disabled) a[href*="http://arxiv.org/"] { background-image: url(../files/arXiv_icon.gif); background-repeat: no-repeat; background-position: right bottom; padding-right: 22px; } */ /* Icon for links to n-category cafe posts (disabled) a[href*="http://golem.ph.utexas.edu/category"] { background-image: url(../files/n-cafe_5.gif); background-repeat: no-repeat; background-position: right bottom; padding-right: 25px; } */ /* Icon for links to pdf files (disabled) a[href$=".pdf"] { background-image: url(../files/pdficon_small.gif); background-repeat: no-repeat; background-position: right bottom; padding-right: 25px; } */ /* Icon for links to pages, etc. -inside- pdf files (disabled) a[href*=".pdf#"] { background-image: url(../files/pdf_entry.gif); background-repeat: no-repeat; background-position: right bottom; padding-right: 25px; } */ a.existingWikiWord { color: #226622; } a.existingWikiWord:visited { color: #226622; } a.existingWikiWord[title] { border: 0px; color: #aa0505; text-decoration: none; } a.existingWikiWord[title]:visited { border: 0px; color: #551111; text-decoration: none; } a[href^="http://"] { border: 0px; color: #003399; } a[href^="http://"]:visited { border: 0px; color: #330066; } a[href^="https://"] { border: 0px; color: #003399; } a[href^="https://"]:visited { border: 0px; color: #330066; } div.dropDown .hide { display: none; } div.dropDown:hover .hide { display:block; } div.clickDown .hide { display: none; } div.clickDown:focus { outline:none; } div.clickDown:focus .hide, div.clickDown:hover .hide { display: block; } div.clickDown .clickToReveal, div.clickDown:focus .clickToHide { display:block; } div.clickDown:focus .clickToReveal, div.clickDown .clickToHide { display:none; } div.clickDown .clickToReveal:after { content: "A(Hover to reveal, click to "hold")"; font-size: 60%; } div.clickDown .clickToHide:after { content: "A(Click to hide)"; font-size: 60%; } div.clickDown .clickToHide, div.clickDown .clickToReveal { white-space: pre-wrap; } .un_theorem, .num_theorem, .un_lemma, .num_lemma, .un_prop, .num_prop, .un_cor, .num_cor, .un_defn, .num_defn, .un_example, .num_example, .un_note, .num_note, .un_remark, .num_remark { margin-left: 1em; } span.theorem_label { margin-left: -1em; } .proof span.theorem_label { margin-left: 0em; } :target { background-color: #BBBBBB; border-radius: 5pt; } /*]]>*/--></style> <script src="/javascripts/prototype.js?1660229990" type="text/javascript"></script> <script src="/javascripts/effects.js?1660229990" type="text/javascript"></script> <script src="/javascripts/dragdrop.js?1660229990" type="text/javascript"></script> <script src="/javascripts/controls.js?1660229990" type="text/javascript"></script> <script src="/javascripts/application.js?1660229990" type="text/javascript"></script> <script src="/javascripts/page_helper.js?1660229990" type="text/javascript"></script> <script src="/javascripts/thm_numbering.js?1660229990" type="text/javascript"></script> <script type="text/x-mathjax-config"> <!--//--><![CDATA[//><!-- MathJax.Ajax.config.path["Contrib"] = "/MathJax"; MathJax.Hub.Config({ MathML: { useMathMLspacing: true }, "HTML-CSS": { scale: 90, extensions: ["handle-floats.js"] } }); MathJax.Hub.Queue( function () { var fos = document.getElementsByTagName('foreignObject'); for (var i = 0; i < fos.length; i++) { MathJax.Hub.Typeset(fos[i]); } }); //--><!]]> </script> <script type="text/javascript"> <!--//--><![CDATA[//><!-- window.addEventListener("DOMContentLoaded", function () { var div = document.createElement('div'); var math = document.createElementNS('http://www.w3.org/1998/Math/MathML', 'math'); document.body.appendChild(div); div.appendChild(math); // Test for MathML support comparable to WebKit version https://trac.webkit.org/changeset/203640 or higher. div.setAttribute('style', 'font-style: italic'); var mathml_unsupported = !(window.getComputedStyle(div.firstChild).getPropertyValue('font-style') === 'normal'); div.parentNode.removeChild(div); if (mathml_unsupported) { // MathML does not seem to be supported... var s = document.createElement('script'); s.src = "https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.7/MathJax.js?config=MML_HTMLorMML-full"; document.querySelector('head').appendChild(s); } else { document.head.insertAdjacentHTML("beforeend", '<style>svg[viewBox] {max-width: 100%}</style>'); } }); //--><!]]> </script> <link href="https://ncatlab.org/nlab/atom_with_headlines" rel="alternate" title="Atom with headlines" type="application/atom+xml" /> <link href="https://ncatlab.org/nlab/atom_with_content" rel="alternate" title="Atom with full content" type="application/atom+xml" /> <script type="text/javascript"> document.observe("dom:loaded", function() { generateThmNumbers(); }); </script> </head> <body> <div id="Container"> <div id="Content"> <h1 id="pageName"> <span style="float: left; margin: 0.5em 0.25em -0.25em 0"> <svg xmlns="http://www.w3.org/2000/svg" width="1.872em" height="1.8em" viewBox="0 0 190 181"> <path fill="#226622" d="M72.8 145c-1.6 17.3-15.7 10-23.6 20.2-5.6 7.3 4.8 15 11.4 15 11.5-.2 19-13.4 26.4-20.3 3.3-3 8.2-4 11.2-7.2a14 14 0 0 0 2.9-11.1c-1.4-9.6-12.4-18.6-16.9-27.2-5-9.6-10.7-27.4-24.1-27.7-17.4-.3-.4 26 4.7 30.7 2.4 2.3 5.4 4.1 7.3 6.9 1.6 2.3 2.1 5.8-1 7.2-5.9 2.6-12.4-6.3-15.5-10-8.8-10.6-15.5-23-26.2-31.8-5.2-4.3-11.8-8-18-3.7-7.3 4.9-4.2 12.9.2 18.5a81 81 0 0 0 30.7 23c3.3 1.5 12.8 5.6 10 10.7-2.5 5.2-11.7 3-15.6 1.1-8.4-3.8-24.3-21.3-34.4-13.7-3.5 2.6-2.3 7.6-1.2 11.1 2.8 9 12.2 17.2 20.9 20.5 17.3 6.7 34.3-8 50.8-12.1z"/> <path fill="#a41e32" d="M145.9 121.3c-.2-7.5 0-19.6-4.5-26-5.4-7.5-12.9-1-14.1 5.8-1.4 7.8 2.7 14.1 4.8 21.3 3.4 12 5.8 29-.8 40.1-3.6-6.7-5.2-13-7-20.4-2.1-8.2-12.8-13.2-15.1-1.9-2 9.7 9 21.2 12 30.1 1.2 4 2 8.8 6.4 10.3 6.9 2.3 13.3-4.7 17.7-8.8 12.2-11.5 36.6-20.7 43.4-36.4 6.7-15.7-13.7-14-21.3-7.2-9.1 8-11.9 20.5-23.6 25.1 7.5-23.7 31.8-37.6 38.4-61.4 2-7.3-.8-29.6-13-19.8-14.5 11.6-6.6 37.6-23.3 49.2z"/> <path fill="#193c78" d="M86.3 47.5c0-13-10.2-27.6-5.8-40.4 2.8-8.4 14.1-10.1 17-1 3.8 11.6-.3 26.3-1.8 38 11.7-.7 10.5-16 14.8-24.3 2.1-4.2 5.7-9.1 11-6.7 6 2.7 7.4 9.2 6.6 15.1-2.2 14-12.2 18.8-22.4 27-3.4 2.7-8 6.6-5.9 11.6 2 4.4 7 4.5 10.7 2.8 7.4-3.3 13.4-16.5 21.7-16 14.6.7 12 21.9.9 26.2-5 1.9-10.2 2.3-15.2 3.9-5.8 1.8-9.4 8.7-15.7 8.9-6.1.1-9-6.9-14.3-9-14.4-6-33.3-2-44.7-14.7-3.7-4.2-9.6-12-4.9-17.4 9.3-10.7 28 7.2 35.7 12 2 1.1 11 6.9 11.4 1.1.4-5.2-10-8.2-13.5-10-11.1-5.2-30-15.3-35-27.3-2.5-6 2.8-13.8 9.4-13.6 6.9.2 13.4 7 17.5 12C70.9 34 75 43.8 86.3 47.4z"/> </svg> </span> <span class="webName">nLab</span> solid state physics </h1> <div class="navigation"> <span class="skipNav"><a href='#navEnd'>Skip the Navigation Links</a> | </span> <span style="display:inline-block; width: 0.3em;"></span> <a href="/nlab/show/HomePage" accesskey="H" title="Home page">Home Page</a> | <a href="/nlab/all_pages" accesskey="A" title="List of all pages">All Pages</a> | <a href="/nlab/latest_revisions" accesskey="U" title="Latest edits and page creations">Latest Revisions</a> | <a href="https://nforum.ncatlab.org/discussion/10892/#Item_8" title="Discuss this page in its dedicated thread on the nForum" style="color: black">Discuss this page</a> | <form accept-charset="utf-8" action="/nlab/search" id="navigationSearchForm" method="get"> <fieldset class="search"><input type="text" id="searchField" name="query" value="Search" style="display:inline-block; float: left;" onfocus="this.value == 'Search' ? this.value = '' : true" onblur="this.value == '' ? this.value = 'Search' : true" /></fieldset> </form> <span id='navEnd'></span> </div> <div id="revision"> <html xmlns="http://www.w3.org/1999/xhtml" xmlns:svg="http://www.w3.org/2000/svg" xml:lang="en" lang="en"> <head><meta http-equiv="Content-type" content="application/xhtml+xml;charset=utf-8" /><title>Contents</title></head> <body> <div class="rightHandSide"> <div class="toc clickDown" tabindex="0"> <h3 id="context">Context</h3> <h4 id="solid_state_physics">Solid state physics</h4> <div class="hide"><div> <ul> <li> <p>basics</p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/Slater+determinant">Slater determinant</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/degeneracy+pressure">degeneracy pressure</a></p> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/crystal">crystal</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/crystallographic+group">crystallographic group</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Bravais+lattice">Bravais lattice</a></p> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Bloch+theory">Bloch theory</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/electronic+band+structure">electronic band structure</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/valence+bundle">valence bundle</a>, <a class="existingWikiWord" href="/nlab/show/conduction+bundle">conduction bundle</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/valence+band">valence band</a>, <a class="existingWikiWord" href="/nlab/show/conduction+band">conduction band</a></p> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Berry+connection">Berry connection</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Berry+phase">Berry phase</a>, <a class="existingWikiWord" href="/nlab/show/Zak+phase">Zak phase</a></li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/phase+of+matter">phase of matter</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/insulator">insulator</a>, <a class="existingWikiWord" href="/nlab/show/topological+insulator">topological insulator</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/metal">metal</a>/<a class="existingWikiWord" href="/nlab/show/conductor">conductor</a>, <a class="existingWikiWord" href="/nlab/show/semi-conductor">semi-conductor</a>, <a class="existingWikiWord" href="/nlab/show/semi-metal">semi-metal</a>,</p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/superconductor">superconductor</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/strange+metal">strange metal</a></p> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/topological+phase+of+matter">topological phase of matter</a>, <a class="existingWikiWord" href="/nlab/show/topological+state+of+matter">topological state of matter</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/symmetry+protected+topological+phase">symmetry protected topological phase</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/K-theory+classification+of+topological+phases+of+matter">K-theory classification of topological phases of matter</a></p> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/topological+order">topological order</a></p> <p><a class="existingWikiWord" href="/nlab/show/anyons">anyons</a></p> </li> <li> <p>Examples</p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/graphene">graphene</a>, <a class="existingWikiWord" href="/nlab/show/Haldane+model">Haldane model</a>,</p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/quantum+Hall+effect">quantum Hall effect</a>)</p> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/AdS-CFT+in+condensed+matter+physics">AdS-CFT in condensed matter physics</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/tensor+network+state">tensor network state</a></li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Levin-Wen+model">Levin-Wen model</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Josephson+effect">Josephson effect</a></p> </li> </ul> </div></div> <h4 id="quantum_systems">Quantum systems</h4> <div class="hide"><div> <p><strong><a class="existingWikiWord" href="/nlab/show/quantum+logic">quantum logic</a></strong></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/linear+logic">linear logic</a>, <a class="existingWikiWord" href="/nlab/show/dependent+linear+type+theory">dependent</a> <a class="existingWikiWord" href="/nlab/show/linear+type+theory">linear type theory</a></p> <p><a class="existingWikiWord" href="/nlab/show/string+diagrams">string diagrams</a> in <a class="existingWikiWord" href="/nlab/show/quantum+information+theory+via+dagger-compact+categories">†-compact categories</a></p> <p><a class="existingWikiWord" href="/nlab/show/tensor+networks">tensor networks</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Bohr+topos">Bohr topos</a></p> <p><a class="existingWikiWord" href="/nlab/show/order-theoretic+structure+in+quantum+mechanics">order-theoretic structure</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/quantum+probability">quantum probability</a></p> </li> </ul> <p><br /></p> <p><strong><a class="existingWikiWord" href="/nlab/show/quantum+physics">quantum physics</a></strong></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/quantum+systems">quantum systems</a></p> <p>(<a class="existingWikiWord" href="/nlab/show/parameterized+quantum+systems">parameterized</a>, <a class="existingWikiWord" href="/nlab/show/open+quantum+system">open</a>)</p> <p><a class="existingWikiWord" href="/nlab/show/quantum+measurement">quantum measurement</a></p> <p><a class="existingWikiWord" href="/nlab/show/quantum+state+collapse">quantum state collapse</a></p> <p><a class="existingWikiWord" href="/nlab/show/quantum+decoherence">quantum decoherence</a></p> <p><a class="existingWikiWord" href="/nlab/show/quantum+adiabatic+theorem">quantum adiabatic theorem</a></p> <p><a class="existingWikiWord" href="/nlab/show/Berry+phases">Berry phases</a></p> <p><a class="existingWikiWord" href="/nlab/show/Dyson+formula">Dyson formula</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/quantum+many-body+physics">quantum many-body physics</a></p> </li> <li> <p><strong><a class="existingWikiWord" href="/nlab/show/quantum+field+theory">quantum field theory</a></strong></p> <p><a class="existingWikiWord" href="/nlab/show/functorial+quantum+field+theory">functorial quantum field theory</a></p> <p><a class="existingWikiWord" href="/nlab/show/algebraic+quantum+field+theory">algebraic quantum field theory</a></p> <p>(<a class="existingWikiWord" href="/nlab/show/non-perturbative+quantum+field+theory">non-</a>)<a class="existingWikiWord" href="/nlab/show/perturbative+quantum+field+theory">perturbative quantum field theory</a></p> </li> <li> <p><strong><a class="existingWikiWord" href="/nlab/show/solid+state+physics">solid state physics</a></strong></p> <p><a class="existingWikiWord" href="/nlab/show/quantum+material">quantum material</a></p> <p>(<a class="existingWikiWord" href="/nlab/show/topological+phases+of+matter">topological</a>) <a class="existingWikiWord" href="/nlab/show/phases+of+matter">phases of matter</a></p> </li> </ul> <p><br /></p> <div> <p><strong><a class="existingWikiWord" href="/nlab/show/quantum+probability+theory">quantum probability theory</a> – <a class="existingWikiWord" href="/nlab/show/observables">observables</a> and <a class="existingWikiWord" href="/nlab/show/states">states</a></strong></p> <ul> <li> <p><strong><a class="existingWikiWord" href="/nlab/show/states">states</a></strong></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/classical+state">classical state</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/quantum+state">quantum state</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/space+of+states+%28in+geometric+quantization%29">space of states (in geometric quantization)</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/state+on+a+star-algebra">state on a star-algebra</a>, <a class="existingWikiWord" href="/nlab/show/quasi-state">quasi-state</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/qbit">qbit</a>, <a class="existingWikiWord" href="/nlab/show/Bell+state">Bell state</a></p> <p><a class="existingWikiWord" href="/nlab/show/dimer">dimer</a>, <a class="existingWikiWord" href="/nlab/show/tensor+network+state">tensor network state</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/quantum+state+preparation">quantum state preparation</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/probability+amplitude">probability amplitude</a>, <a class="existingWikiWord" href="/nlab/show/quantum+fluctuation">quantum fluctuation</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/pure+state">pure state</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/wave+function">wave function</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/bra-ket">bra-ket</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Bell+state">Bell state</a></p> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/quantum+superposition">quantum superposition</a>, <a class="existingWikiWord" href="/nlab/show/quantum+interference">quantum interference</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/quantum+entanglement">quantum entanglement</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/quantum+measurement">quantum measurement</a></p> <p><a class="existingWikiWord" href="/nlab/show/wave+function+collapse">wave function collapse</a></p> <p><a class="existingWikiWord" href="/nlab/show/Born+rule">Born rule</a></p> <p><a class="existingWikiWord" href="/nlab/show/deferred+measurement+principle">deferred measurement principle</a></p> <p><a class="existingWikiWord" href="/nlab/show/quantum+reader+monad">quantum reader monad</a></p> <p><a class="existingWikiWord" href="/nlab/show/measurement+problem">measurement problem</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/superselection+sector">superselection sector</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/mixed+state">mixed state</a>, <a class="existingWikiWord" href="/nlab/show/density+matrix">density matrix</a></p> <p><a class="existingWikiWord" href="/nlab/show/entanglement+entropy">entanglement entropy</a></p> <p><a class="existingWikiWord" href="/nlab/show/holographic+entanglement+entropy">holographic entanglement entropy</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/coherent+quantum+state">coherent quantum state</a></p> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/ground+state">ground state</a>, <a class="existingWikiWord" href="/nlab/show/excited+state">excited state</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/quasi-free+state">quasi-free state</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Fock+space">Fock space</a>, <a class="existingWikiWord" href="/nlab/show/second+quantization">second quantization</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/vacuum">vacuum</a>, <a class="existingWikiWord" href="/nlab/show/vacuum+state">vacuum state</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/Hadamard+state">Hadamard state</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/vacuum+diagram">vacuum diagram</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/vacuum+expectation+value">vacuum expectation value</a>, <a class="existingWikiWord" href="/nlab/show/vacuum+amplitude">vacuum amplitude</a>, <a class="existingWikiWord" href="/nlab/show/vacuum+fluctuation">vacuum fluctuation</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/vacuum+energy">vacuum energy</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/vacuum+polarization">vacuum polarization</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/interacting+vacuum">interacting vacuum</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/thermal+vacuum">thermal vacuum</a>, <a class="existingWikiWord" href="/nlab/show/KMS+state">KMS state</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/vacuum+stability">vacuum stability</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/false+vacuum">false vacuum</a>, <a class="existingWikiWord" href="/nlab/show/tachyon">tachyon</a>, <a class="existingWikiWord" href="/nlab/show/Coleman-De+Luccia+instanton">Coleman-De Luccia instanton</a></li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/theta+vacuum">theta vacuum</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/perturbative+string+theory+vacuum">perturbative string theory vacuum</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/non-geometric+string+theory+vacuum">non-geometric string theory vacuum</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/landscape+of+string+theory+vacua">landscape of string theory vacua</a></p> </li> </ul> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/entangled+state">entangled state</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/tensor+network+state">tensor network state</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/matrix+product+state">matrix product state</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/tree+tensor+network+state">tree tensor network state</a></p> </li> </ul> </li> </ul> </li> <li> <p><strong><a class="existingWikiWord" href="/nlab/show/observables">observables</a></strong></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/quantum+observable">quantum observable</a>, <a class="existingWikiWord" href="/nlab/show/beable">beable</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/algebra+of+observables">algebra of observables</a>, <a class="existingWikiWord" href="/nlab/show/star-algebra">star-algebra</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Bohr+topos">Bohr topos</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/quantum+operator+%28in+geometric+quantization%29">quantum operator (in geometric quantization)</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/quantum+operation">quantum operation</a>, <a class="existingWikiWord" href="/nlab/show/quantum+effect">quantum effect</a>, <a class="existingWikiWord" href="/nlab/show/effect+algebra">effect algebra</a></p> </li> <li> <p>in <a class="existingWikiWord" href="/nlab/show/quantum+field+theory">quantum field theory</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/local+observable">local observable</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/polynomial+observable">polynomial observable</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/linear+observable">linear observable</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/field+observable">field observable</a></li> </ul> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/regular+observable">regular observable</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/microcausal+observable">microcausal observable</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/normal-ordered+product">normal-ordered product</a>, <a class="existingWikiWord" href="/nlab/show/time-ordered+products">time-ordered products</a>, <a class="existingWikiWord" href="/nlab/show/retarded+product">retarded product</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Wick+algebra">Wick algebra</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/scattering+amplitude">scattering amplitude</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/interacting+field+algebra+of+observables">interacting field algebra of observables</a>, <a class="existingWikiWord" href="/nlab/show/Bogoliubov%27s+formula">Bogoliubov's formula</a></p> </li> </ul> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/GNS+construction">GNS construction</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/theorems">theorems</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/order-theoretic+structure+in+quantum+mechanics">order-theoretic structure in quantum mechanics</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/Gleason%27s+theorem">Gleason's theorem</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Alfsen-Shultz+theorem">Alfsen-Shultz theorem</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Harding-D%C3%B6ring-Hamhalter+theorem">Harding-Döring-Hamhalter theorem</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Kochen-Specker+theorem">Kochen-Specker theorem</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Nuiten%27s+lemma">Nuiten's lemma</a></p> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Wigner%27s+theorem">Wigner's theorem</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/no-cloning+theorem">no-cloning theorem</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Bell%27s+theorem">Bell's theorem</a></p> </li> </ul> </li> </ul> </div> <p><br /></p> <p><strong><a class="existingWikiWord" href="/nlab/show/quantum+information">quantum information</a></strong></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/quantum+information+via+dagger-compact+categories">quantum information via dagger-compact categories</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/quantum+operation">quantum operation</a>, <a class="existingWikiWord" href="/nlab/show/quantum+channel">quantum channel</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/quantum+teleportation">quantum teleportation</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/quantum+entanglement">quantum entanglement</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/entanglement+entropy">entanglement entropy</a></p> <p><a class="existingWikiWord" href="/nlab/show/holographic+entanglement+entropy">holographic entanglement entropy</a></p> <p><a class="existingWikiWord" href="/nlab/show/topological+entanglement+entropy">topological entanglement entropy</a></p> </li> </ul> <p><br /></p> <p><strong><a class="existingWikiWord" href="/nlab/show/quantum+computation">quantum computation</a></strong></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/adiabatic+quantum+computation">adiabatic quantum computation</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/measurement-based+quantum+computation">measurement-based quantum computation</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/topological+quantum+computation">topological quantum computation</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/quantum+gate">quantum gate</a>, <a class="existingWikiWord" href="/nlab/show/quantum+circuit">quantum circuit</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/quantum+programming+language">quantum programming language</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/quantum+error+correction">quantum error correction</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/HaPPY+code">HaPPY code</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Majorana+dimer+code">Majorana dimer code</a></p> </li> </ul> </li> </ul> <p><a class="existingWikiWord" href="/nlab/show/qbit">qbit</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/spin+resonance+qbit">spin resonance qbit</a></li> </ul> <p>quantum algorithms:</p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/Grover%27s+algorithm">Grover's algorithm</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Shor%27s+algorithm">Shor's algorithm</a></p> </li> </ul> <p><br /></p> <p><strong><a class="existingWikiWord" href="/nlab/show/quantum+sensing">quantum sensing</a></strong></p> <p><br /></p> <p><strong><a class="existingWikiWord" href="/nlab/show/quantum+communication">quantum communication</a></strong></p> </div></div> </div> </div> <h1 id="contents">Contents</h1> <div class='maruku_toc'> <ul> <li><a href='#idea'>Idea</a></li> <li><a href='#properties'>Properties</a></li> <ul> <li><a href='#topological_phases_of_matter'>Topological phases of matter</a></li> </ul> <li><a href='#related_concepts'>Related concepts</a></li> <li><a href='#references'>References</a></li> <ul> <li><a href='#general'>General</a></li> <li><a href='#examples_and_applications'>Examples and applications</a></li> <li><a href='#adscmt_correspondence'>AdS/CMT correspondence</a></li> <li><a href='#ktheory_classification_of_gapped_topological_phases_of_matter'>K-Theory classification of gapped topological phases of matter</a></li> <li><a href='#tensor_networks_in_solid_state_physics'>Tensor networks in solid state physics</a></li> </ul> </ul> </div> <h2 id="idea">Idea</h2> <p>The <a class="existingWikiWord" href="/nlab/show/physics">physics</a> of <a class="existingWikiWord" href="/nlab/show/solid">solid</a> condensed <a class="existingWikiWord" href="/nlab/show/matter">matter</a> (made of <a class="existingWikiWord" href="/nlab/show/fermions">fermions</a>, due to the <a class="existingWikiWord" href="/nlab/show/Pauli+exclusion+principle">Pauli exclusion principle</a>), also <em><a class="existingWikiWord" href="/nlab/show/continuum+mechanics">continuum mechanics</a></em>.</p> <h2 id="properties">Properties</h2> <h3 id="topological_phases_of_matter">Topological phases of matter</h3> <p>See at <em><a class="existingWikiWord" href="/nlab/show/K-theory+classification+of+topological+phases+of+matter">K-theory classification of topological phases of matter</a></em>.</p> <h2 id="related_concepts">Related concepts</h2> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/quantum+many-body+physics">quantum many-body physics</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/mean-field+theory">mean-field theory</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/mathematical+physics">mathematical physics</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/high+energy+physics">high energy physics</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Bloch%27s+theorem">Bloch's theorem</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/phonon">phonon</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/degeneracy+pressure">degeneracy pressure</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Bose-Einstein+condensate">Bose-Einstein condensate</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Levin-Wen+model">Levin-Wen model</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/quantum+material">quantum material</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/superconductivity">superconductivity</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/topological+phases+of+matter">topological phases of matter</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/topological+order">topological order</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/symmetry+protected+trivial+order">symmetry protected trivial order</a></p> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/AdS-CFT+in+condensed+matter+physics">AdS-CFT in condensed matter physics</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/phase+of+matter">phase of matter</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Josephson+effect">Josephson effect</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/mesoscopic+physics">mesoscopic physics</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/high+energy+physics">high energy physics</a>, <a class="existingWikiWord" href="/nlab/show/nuclear+physics">nuclear physics</a></p> </li> </ul> <h2 id="references">References</h2> <h3 id="general">General</h3> <p>Textbook accounts:</p> <ul> <li id="Kittel53"> <p><a class="existingWikiWord" href="/nlab/show/Charles+Kittel">Charles Kittel</a>, <em>Introduction to Solid State Physics</em>, Wiley (1953-) <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mo stretchy="false">[</mo></mrow><annotation encoding="application/x-tex">[</annotation></semantics></math><a href="https://www.wiley.com/en-us/Introduction+to+Solid+State+Physics%2C+8th+Edition-p-9780471415268">ISBN:978-0-471-41526-8</a>, <a href="http://metal.elte.hu/~groma/Anyagtudomany/kittel.pdf">pdf</a>, <a href="https://en.wikipedia.org/wiki/Introduction_to_Solid_State_Physics">Wikipedia entry</a><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">]</annotation></semantics></math></p> </li> <li id="JS75"> <p><a class="existingWikiWord" href="/nlab/show/John+Slater">John Slater</a>, <em>Solid-State and Molecular Theory: A Scientific Biography</em>, Wiley (1975) [<a href="https://archive.org/details/solidstatemolecu00slat/">archive</a>]</p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Neil+Ashcroft">Neil Ashcroft</a>, <a class="existingWikiWord" href="/nlab/show/N.+David+Mermin">N. David Mermin</a>, <em>Solid State Physics</em>, Saunders College Publishing (1973) [<a href="https://archive.org/details/AshcroftSolidState">archive</a>, <a href="https://en.wikipedia.org/wiki/Ashcroft_and_Mermin">Wikipedia entry</a>]</p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/John+W.+Negele">John W. Negele</a>, <a class="existingWikiWord" href="/nlab/show/Henri+Orland">Henri Orland</a>, <em>Quantum Many-Particle Systems</em>, Westview Press (1988, 1998) [<a href="https://doi.org/10.1201/9780429497926">doi:10.1201/9780429497926</a>]</p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Naoto+Nagaosa">Naoto Nagaosa</a>, <em>Quantum Field Theory in Condensed Matter Physics</em>, Texts and Monographs in Physics, Springer (1999) [<a href="https://doi.org/10.1007/978-3-662-03774-4_2">doi:10.1007/978-3-662-03774-4_2</a>]</p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Alexander+L.+Fetter">Alexander L. Fetter</a>, <a class="existingWikiWord" href="/nlab/show/John+Dirk+Walecka">John Dirk Walecka</a>, <em>Quantum theory of many-particle systems</em>, Mcgraw-Hill (1991); Dover (2003) [<a href="https://archive.org/details/quantum-theory-of-many-particle-systems-by-alexander-l.-fetter-john-dirk-walecka-physics-z-lib.org/mode/thumb">archive.org</a>]</p> </li> <li id="Roessler04"> <p><a class="existingWikiWord" href="/nlab/show/Ulrich+R%C3%B6%C3%9Fler">Ulrich Rößler</a>, <em>Solid State Theory: An Introduction</em>, Springer (2004, 2009) <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mo stretchy="false">[</mo></mrow><annotation encoding="application/x-tex">[</annotation></semantics></math><a href="https://link.springer.com/book/10.1007/978-3-540-92762-4">doi:10.1007/978-3-540-92762-4</a><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">]</annotation></semantics></math></p> </li> </ul> <p>In terms of <a class="existingWikiWord" href="/nlab/show/quantum+field+theory">quantum field theory</a>:</p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/Eduardo+Fradkin">Eduardo Fradkin</a>, <em>Field Theories of Condensed Matter Physics</em>, Cambridge University Press (2013) [ISBN: 9781139015509, <a href="https://doi.org/10.1017/CBO9781139015509">doi:10.1017/CBO9781139015509</a>]</p> </li> <li> <p>Eduardo C. Marino, <em>Quantum Field Theory Approach to Condensed Matter Physics</em>, Cambridge University Press (2017) [<a href="https://doi.org/10.1017/9781139696548">doi:10.1017/9781139696548</a>]</p> </li> </ul> <p>With an emphasis on <a class="existingWikiWord" href="/nlab/show/non-perturbative+quantum+field+theory">non-perturbative quantum field theory</a>:</p> <ul> <li>Alvaro Ferraz, <a class="existingWikiWord" href="/nlab/show/Kumar+S.+Gupta">Kumar S. Gupta</a>, Gordon W. Semenoff, Pasquale Sodano (eds.): <em>Strongly Coupled Field Theories for Condensed Matter and Quantum Information Theory</em>, Springer Proceedings in Physics <strong>239</strong>, Springer (2020) [<a href="https://doi.org/10.1007/978-3-030-35473-2">doi:10.1007/978-3-030-35473-2</a>, <a href="https://link.springer.com/content/pdf/10.1007/978-3-030-35473-2.pdf">pdf</a>]</li> </ul> <p>Lecture notes:</p> <ul> <li id="Tong2017"><a class="existingWikiWord" href="/nlab/show/David+Tong">David Tong</a>, <em>Lectures on solid state physics</em> (2017) <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mo stretchy="false">[</mo></mrow><annotation encoding="application/x-tex">[</annotation></semantics></math><a href="http://www.damtp.cam.ac.uk/user/tong/aqm/solidstate.pdf">pdf</a>, <a href="http://www.damtp.cam.ac.uk/user/tong/solidstate.html">webpage</a><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">]</annotation></semantics></math></li> </ul> <p>Specifically on <a class="existingWikiWord" href="/nlab/show/Bloch-Floquet+theory">Bloch-Floquet theory</a>:</p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Michael+Reed">Michael Reed</a>, <a class="existingWikiWord" href="/nlab/show/Barry+Simon">Barry Simon</a>, Sec. XIII.16 <em>Schrödinger operators with periodic potentials</em>, of: <em><a class="existingWikiWord" href="/nlab/show/Methods+of+Modern+Mathematical+Physics">Methods of Modern Mathematical Physics</a> – IV: Analysis of Operators</em>, Academic Press (1978) <p>(<a href="https://www.elsevier.com/books/iv-analysis-of-operators/reed/978-0-08-057045-7">ISBN:9780080570457</a>)</p> </li> </ul> <p>With focus on <a class="existingWikiWord" href="/nlab/show/semiconductor">semiconductor</a>-theory:</p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/Karlheinz+Seeger">Karlheinz Seeger</a>, <em>Semiconductor Physics</em>, Advanced texts in physics, Springer (2004) <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mo stretchy="false">[</mo></mrow><annotation encoding="application/x-tex">[</annotation></semantics></math><a href="https://doi.org/10.1007/978-3-662-09855-4">doi:10.1007/978-3-662-09855-4</a><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">]</annotation></semantics></math></p> </li> <li id="Li06"> <p><a class="existingWikiWord" href="/nlab/show/Sheng+San+Li">Sheng San Li</a>, <em>Semiconductor Physical Electronics</em>, Springer (2006) 61-104 <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mo stretchy="false">[</mo></mrow><annotation encoding="application/x-tex">[</annotation></semantics></math><a href="https://link.springer.com/book/10.1007/0-387-37766-2">doi:10.1007/0-387-37766-2</a><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">]</annotation></semantics></math></p> </li> </ul> <p>See also:</p> <ul> <li>Wikipedia, <em><a href="http://en.wikipedia.org/wiki/Solid_state_physics">Solid state physics</a></em></li> </ul> <p>and maybe also</p> <ul> <li id="LandauLifshitz59"><a class="existingWikiWord" href="/nlab/show/Lev+Landau">Lev Landau</a>, <a class="existingWikiWord" href="/nlab/show/Evgeny+Lifshitz">Evgeny Lifshitz</a>, <em>Theory of Elasticity</em>, part VII of <em><a class="existingWikiWord" href="/nlab/show/Course+of+Theoretical+Physics">Course of Theoretical Physics</a></em>, 1959, 1970</li> </ul> <h3 id="examples_and_applications">Examples and applications</h3> <p>Discussion of possible realization of the <a class="existingWikiWord" href="/nlab/show/SYK-model">SYK-model</a> in <a class="existingWikiWord" href="/nlab/show/condensed+matter+physics">condensed matter physics</a>:</p> <ul> <li>D. I. Pikulin, M. Franz, <em>Black hole on a chip: proposal for a physical realization of the SYK model in a solid-state system</em>, Phys. Rev. X 7, 031006 (2017) (<a href="https://arxiv.org/abs/1702.04426">arXiv:1702.04426</a>)</li> </ul> <h3 id="adscmt_correspondence">AdS/CMT correspondence</h3> <p>On <a class="existingWikiWord" href="/nlab/show/AdS%2FCFT+in+condensed+matter+physics">AdS/CFT in condensed matter physics</a>:</p> <ul> <li id="HartnollLucasSachdev16"><a class="existingWikiWord" href="/nlab/show/Sean+Hartnoll">Sean Hartnoll</a>, <a class="existingWikiWord" href="/nlab/show/Andrew+Lucas">Andrew Lucas</a>, <a class="existingWikiWord" href="/nlab/show/Subir+Sachdev">Subir Sachdev</a>, <em>Holographic quantum matter</em>, MIT Press 2018 (<a href="https://arxiv.org/abs/1612.07324">arXiv:1612.07324</a>, <a href="https://mitpress.ublish.com/book/holographic-quantum-matter">publisher</a>)</li> </ul> <p>Proposed realization of aspects of <a class="existingWikiWord" href="/nlab/show/p-adic+AdS%2FCFT+correspondence">p-adic AdS/CFT correspondence</a> in <a class="existingWikiWord" href="/nlab/show/solid+state+physics">solid state physics</a>:</p> <ul> <li>Gregory Bentsen, Tomohiro Hashizume, Anton S. Buyskikh, Emily J. Davis, Andrew J. Daley, <a class="existingWikiWord" href="/nlab/show/Steven+Gubser">Steven Gubser</a>, Monika Schleier-Smith, <em>Treelike interactions and fast scrambling with cold atoms</em>, Phys. Rev. Lett. 123, 130601 (2019) (<a href="https://arxiv.org/abs/1905.11430">arXiv:1905.11430</a>)</li> </ul> <h3 id="ktheory_classification_of_gapped_topological_phases_of_matter">K-Theory classification of gapped topological phases of matter</h3> <p>Classification of <a class="existingWikiWord" href="/nlab/show/condensed+matter+physics">condensed matter</a> with <a class="existingWikiWord" href="/nlab/show/gapped+Hamiltonians">gapped Hamiltonians</a> (<a class="existingWikiWord" href="/nlab/show/topological+insulators">topological insulators</a>, <a class="existingWikiWord" href="/nlab/show/topological+phases+of+matter">topological phases of matter</a>) by <a class="existingWikiWord" href="/nlab/show/twisted+K-theory">twisted</a> <a class="existingWikiWord" href="/nlab/show/equivariant+K-theory">equivariant</a> <a class="existingWikiWord" href="/nlab/show/topological+K-theory">topological K-theory</a>:</p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/Alexei+Kitaev">Alexei Kitaev</a>, <em>Periodic table for topological insulators and superconductors</em>, talk at: L.D.Landau Memorial Conference “Advances in Theoretical Physics”, June 22-26, 2008, In:AIP Conference Proceedings 1134, 22 (2009) (<a href="https://arxiv.org/abs/0901.2686">arXiv:0901.2686</a>, <a href="https://doi.org/10.1063/1.3149495">doi:10.1063/1.3149495</a>)</p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Daniel+Freed">Daniel Freed</a>, <a class="existingWikiWord" href="/nlab/show/Gregory+Moore">Gregory Moore</a>, <em>Twisted equivariant matter</em>, Ann. Henri Poincaré (2013) 14: 1927 (<a href="https://arxiv.org/abs/1208.5055">arXiv:1208.5055</a>)</p> </li> <li> <p>Guo Chuan Thiang, <em>On the K-theoretic classification of topological phases of matter</em>, Annales Henri Poincare 17(4) 757-794 (2016) (<a href="https://arxiv.org/abs/1406.7366">arXiv:1406.7366</a>)</p> </li> <li> <p>Ralph M. Kaufmann, Dan Li, Birgit Wehefritz-Kaufmann, <em>Topological insulators and K-theory</em> (<a href="https://arxiv.org/abs/1510.08001">arXiv:1510.08001</a>, <a href="http://inspirehep.net/record/1401095/">spire:1401095/</a>)</p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Daniel+Freed">Daniel Freed</a>, <a class="existingWikiWord" href="/nlab/show/Michael+Hopkins">Michael Hopkins</a>, <em>Reflection positivity and invertible topological phases</em> (<a href="https://arxiv.org/abs/1604.06527">arXiv:1604.06527</a>)</p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Daniel+Freed">Daniel Freed</a>, <em>Lectures on field theory and topology</em> (<a href="https://cds.cern.ch/record/2699265">cds:2699265</a>)</p> </li> <li> <p>Charles Zhaoxi Xiong, <em>Classification and Construction of Topological Phases of Quantum Matter</em> (<a href="https://arxiv.org/abs/1906.02892">arXiv:1906.02892</a>)</p> </li> </ul> <h3 id="tensor_networks_in_solid_state_physics">Tensor networks in solid state physics</h3> <p>Discussion of exotic <a class="existingWikiWord" href="/nlab/show/phases+of+matter">phases of matter</a> via <a class="existingWikiWord" href="/nlab/show/tensor+network+states">tensor network states</a>:</p> <p>General:</p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/Roman+Orus">Roman Orus</a>, <em>A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States</em>, Annals of Physics 349 (2014) 117-158 (<a href="https://arxiv.org/abs/1306.2164">arXiv:1306.2164</a>)</p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Jens+Eisert">Jens Eisert</a>, <em>Entanglement and tensor network states</em>, Modeling and Simulation 3, 520 (2013) (<a href="https://arxiv.org/abs/1308.3318">arXiv:1308.3318</a>)</p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Thorsten+B.+Wahl">Thorsten B. Wahl</a>, <em>Tensor network states for the description of quantum many-body systems</em> (<a href="https://arxiv.org/abs/1509.05984">arXiv:1509.05984</a>)</p> </li> </ul> <p>Specifically <a class="existingWikiWord" href="/nlab/show/tree+tensor+networks">tree tensor networks</a>:</p> <ul> <li>Valentin Murg, Örs Legeza, Reinhard M. Noack, Frank Verstraete, <em>Simulating Strongly Correlated Quantum Systems with Tree Tensor Networks</em>, Phys. Rev. B 82, 205105 (2010) (<a href="https://arxiv.org/abs/1006.3095">arXiv:1006.3095</a>)</li> </ul> <p>Concrete materials:</p> <ul> <li>A. Kshetrimayum, C. Balz, B. Lake, <a class="existingWikiWord" href="/nlab/show/Jens+Eisert">Jens Eisert</a>, <em>Tensor network investigation of the double layer Kagome compound <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><msub><mi>Ca</mi> <mn>10</mn></msub><msub><mi>Cr</mi> <mn>7</mn></msub><msub><mi>O</mi> <mn>28</mn></msub></mrow><annotation encoding="application/x-tex">Ca_{10} Cr_{7} O_{28}</annotation></semantics></math></em> (<a href="https://arxiv.org/abs/1904.00028">arXiv:1904.00028</a>)</li> </ul> </body></html> </div> <div class="revisedby"> <p> Last revised on August 18, 2024 at 18:07:43. See the <a href="/nlab/history/solid+state+physics" style="color: #005c19">history</a> of this page for a list of all contributions to it. </p> </div> <div class="navigation navfoot"> <a href="/nlab/edit/solid+state+physics" accesskey="E" class="navlink" id="edit" rel="nofollow">Edit</a><a href="https://nforum.ncatlab.org/discussion/10892/#Item_8">Discuss</a><span class="backintime"><a href="/nlab/revision/solid+state+physics/44" accesskey="B" class="navlinkbackintime" id="to_previous_revision" rel="nofollow">Previous revision</a></span><a href="/nlab/show/diff/solid+state+physics" accesskey="C" class="navlink" id="see_changes" rel="nofollow">Changes from previous revision</a><a href="/nlab/history/solid+state+physics" accesskey="S" class="navlink" id="history" rel="nofollow">History (44 revisions)</a> <a href="/nlab/show/solid+state+physics/cite" style="color: black">Cite</a> <a href="/nlab/print/solid+state+physics" accesskey="p" id="view_print" rel="nofollow">Print</a> <a href="/nlab/source/solid+state+physics" id="view_source" rel="nofollow">Source</a> </div> </div> <!-- Content --> </div> <!-- Container --> </body> </html>