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href="https://www.academia.edu/30269806/A_density_matrix_renormalisation_group_algorithm_for_quantum_lattice_systems_with_a_large_number_of_states_per_site"><img alt="Research paper thumbnail of A density matrix renormalisation group algorithm for quantum lattice systems with a large number of states per site" class="work-thumbnail" src="https://attachments.academia-assets.com/50736768/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/30269806/A_density_matrix_renormalisation_group_algorithm_for_quantum_lattice_systems_with_a_large_number_of_states_per_site">A density matrix renormalisation group algorithm for quantum lattice systems with a large number of states per site</a></div><div class="wp-workCard_item"><span>Phys Rev B</span><span>, 1999</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">A variant of White's density matrix renormalisation group scheme which is designed to compute low...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">A variant of White's density matrix renormalisation group scheme which is designed to compute low-lying energies of one-dimensional quantum lattice models with a large number of degrees of freedom per site is described. The method is tested on two exactly solvable models---the spin-1/2 antiferromagnetic Heisenberg chain and a dimerised XY spin chain. To illustrate the potential of the method, it is applied to a model of spins interacting with quantum phonons. It is shown that the method accurately resolves a number of energy gaps on periodic rings which are sufficiently large to afford an accurate investigation of critical properties via the use of finite-size scaling theory.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="b285159a5ffc066b0bcf694aae174ede" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":50736768,"asset_id":30269806,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/50736768/download_file?st=MTczMjQ1MjAxNyw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="30269806"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="30269806"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 30269806; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=30269806]").text(description); $(".js-view-count[data-work-id=30269806]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 30269806; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='30269806']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 30269806, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "b285159a5ffc066b0bcf694aae174ede" } } $('.js-work-strip[data-work-id=30269806]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":30269806,"title":"A density matrix renormalisation group algorithm for quantum lattice systems with a large number of states per site","translated_title":"","metadata":{"abstract":"A variant of White's density matrix renormalisation group scheme which is designed to compute low-lying energies of one-dimensional quantum lattice models with a large number of degrees of freedom per site is described. 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="30269805"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/30269805/One_dimensional_continuum_Falicov_Kimball_model_in_the_strongly_correlated_limit"><img alt="Research paper thumbnail of One dimensional continuum Falicov-Kimball model in the strongly correlated limit" class="work-thumbnail" src="https://attachments.academia-assets.com/50736787/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/30269805/One_dimensional_continuum_Falicov_Kimball_model_in_the_strongly_correlated_limit">One dimensional continuum Falicov-Kimball model in the strongly correlated limit</a></div><div class="wp-workCard_item"><span>Physica A: Statistical Mechanics and its Applications</span><span>, 1994</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="fb650ed486f12056598f2abca8333f07" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":50736787,"asset_id":30269805,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/50736787/download_file?st=MTczMjQ1MjAxNyw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="30269805"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="30269805"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 30269805; 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In the ground state it is found that the f electrons form a cluster. The effect of including a Takahashi repulsion between f particles is also studied where it is found that as the repulsion is increased the ground state f electron configuration changes discontinuously from the clustered configuration to a homogeneous or equal spaced configuration analogous to the checkerboard configuration which arises in the lattice Falicov-Kimball model.","publication_date":{"day":null,"month":null,"year":1994,"errors":{}},"publication_name":"Physica A: Statistical Mechanics and its Applications","grobid_abstract_attachment_id":50736787},"translated_abstract":null,"internal_url":"https://www.academia.edu/30269805/One_dimensional_continuum_Falicov_Kimball_model_in_the_strongly_correlated_limit","translated_internal_url":"","created_at":"2016-12-05T23:12:54.415-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":57527093,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":50736787,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/50736787/thumbnails/1.jpg","file_name":"9407055.pdf","download_url":"https://www.academia.edu/attachments/50736787/download_file?st=MTczMjQ1MjAxNyw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"One_dimensional_continuum_Falicov_Kimbal.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/50736787/9407055-libre.pdf?1481008997=\u0026response-content-disposition=attachment%3B+filename%3DOne_dimensional_continuum_Falicov_Kimbal.pdf\u0026Expires=1732455617\u0026Signature=Rz~yfRh3TVu4YQjFBcI03FuCIFriFPLBOmd~W~~5cqTJyNkkEl3m1iUDplJj6dNQPA~9RAoa9HQMNRxu7rbX0YaJ-a90ZICKdMvOyw2F2IhWUHfzgqCIHVdfcv0YZuRV2iKqnH0i9xDqujpK~LTakLdjUQfksKBxP5EIIjX5xxC9HDrc3R6EWRCg7gD8I1J0NZBQbn~q~gIKNVw3QgLhjh7Fh5znjIwC92t2GxYYM0RIGRG6FN6AlX3vlhYX6c51Pc6tcQG9E-vIR7PUOYdnXxn22hO1EkiS0wIr0RqYxQWwVaObqBScdEIjr2OLcYOJp58g9Qvik0MDCHZJ3L44sg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"One_dimensional_continuum_Falicov_Kimball_model_in_the_strongly_correlated_limit","translated_slug":"","page_count":18,"language":"en","content_type":"Work","owner":{"id":57527093,"first_name":"Robert","middle_initials":null,"last_name":"Bursill","page_name":"RobertBursill","domain_name":"independent","created_at":"2016-12-01T17:26:12.952-08:00","display_name":"Robert Bursill","url":"https://independent.academia.edu/RobertBursill"},"attachments":[{"id":50736787,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/50736787/thumbnails/1.jpg","file_name":"9407055.pdf","download_url":"https://www.academia.edu/attachments/50736787/download_file?st=MTczMjQ1MjAxNyw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"One_dimensional_continuum_Falicov_Kimbal.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/50736787/9407055-libre.pdf?1481008997=\u0026response-content-disposition=attachment%3B+filename%3DOne_dimensional_continuum_Falicov_Kimbal.pdf\u0026Expires=1732455617\u0026Signature=Rz~yfRh3TVu4YQjFBcI03FuCIFriFPLBOmd~W~~5cqTJyNkkEl3m1iUDplJj6dNQPA~9RAoa9HQMNRxu7rbX0YaJ-a90ZICKdMvOyw2F2IhWUHfzgqCIHVdfcv0YZuRV2iKqnH0i9xDqujpK~LTakLdjUQfksKBxP5EIIjX5xxC9HDrc3R6EWRCg7gD8I1J0NZBQbn~q~gIKNVw3QgLhjh7Fh5znjIwC92t2GxYYM0RIGRG6FN6AlX3vlhYX6c51Pc6tcQG9E-vIR7PUOYdnXxn22hO1EkiS0wIr0RqYxQWwVaObqBScdEIjr2OLcYOJp58g9Qvik0MDCHZJ3L44sg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":318,"name":"Mathematical Physics","url":"https://www.academia.edu/Documents/in/Mathematical_Physics"},{"id":518,"name":"Quantum Physics","url":"https://www.academia.edu/Documents/in/Quantum_Physics"},{"id":522,"name":"Thermodynamics","url":"https://www.academia.edu/Documents/in/Thermodynamics"},{"id":277776,"name":"Quantum and classical statistical mechanics","url":"https://www.academia.edu/Documents/in/Quantum_and_classical_statistical_mechanics"}],"urls":[]}, dispatcherData: dispatcherData }); 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R .J.B ursi l l SchoolofPhysics,U niversity ofN ew South W al es,Sydney, N SW 2052,A ustral ia.","publication_date":{"day":null,"month":null,"year":1998,"errors":{}},"publication_name":"Physical Review B","grobid_abstract_attachment_id":50667581},"translated_abstract":null,"internal_url":"https://www.academia.edu/30208968/Identification_of_excitons_in_conjugated_polymers_A_density_matrix_renormalization_group_study","translated_internal_url":"","created_at":"2016-12-01T17:42:16.913-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":57527093,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":50667581,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/50667581/thumbnails/1.jpg","file_name":"9802216.pdf","download_url":"https://www.academia.edu/attachments/50667581/download_file?st=MTczMjQ1MjAxNyw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Identification_of_excitons_in_conjugated.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/50667581/9802216-libre.pdf?1480643653=\u0026response-content-disposition=attachment%3B+filename%3DIdentification_of_excitons_in_conjugated.pdf\u0026Expires=1732455617\u0026Signature=FJQOq1jZ3ycC7DKopslk~E-0Xo5JsJqcpDfAha6tUNXKEy-Lejr2iw1eTjylz4x5ztBuEoATaZxkAu3XZgpQ8~bfxBXUgol4TTWAnPm5elTxaMvuKJpKSHVnhNKz5G6cjhFxb5IcsaYbvEx1dMdcupP8iyOV181synFTVvuJjZ1Fm2ll5uZ486Fuu9fkcxiYxJoe83w1z~cGKGs9R20TaMy2XyUnffCekBRpOyrXZqsaSpI5sCQhUZC5m9yVLWFzMIpgTs~zBGgK9ltwAjsdkBhLhm6lzBZ2tV9ZPoxcseFbVrq6X~91u82VjDUyxxrpKHXhX7nUwAmBScsc2UHcMw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Identification_of_excitons_in_conjugated_polymers_A_density_matrix_renormalization_group_study","translated_slug":"","page_count":11,"language":"en","content_type":"Work","owner":{"id":57527093,"first_name":"Robert","middle_initials":null,"last_name":"Bursill","page_name":"RobertBursill","domain_name":"independent","created_at":"2016-12-01T17:26:12.952-08:00","display_name":"Robert Bursill","url":"https://independent.academia.edu/RobertBursill"},"attachments":[{"id":50667581,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/50667581/thumbnails/1.jpg","file_name":"9802216.pdf","download_url":"https://www.academia.edu/attachments/50667581/download_file?st=MTczMjQ1MjAxNyw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Identification_of_excitons_in_conjugated.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/50667581/9802216-libre.pdf?1480643653=\u0026response-content-disposition=attachment%3B+filename%3DIdentification_of_excitons_in_conjugated.pdf\u0026Expires=1732455617\u0026Signature=FJQOq1jZ3ycC7DKopslk~E-0Xo5JsJqcpDfAha6tUNXKEy-Lejr2iw1eTjylz4x5ztBuEoATaZxkAu3XZgpQ8~bfxBXUgol4TTWAnPm5elTxaMvuKJpKSHVnhNKz5G6cjhFxb5IcsaYbvEx1dMdcupP8iyOV181synFTVvuJjZ1Fm2ll5uZ486Fuu9fkcxiYxJoe83w1z~cGKGs9R20TaMy2XyUnffCekBRpOyrXZqsaSpI5sCQhUZC5m9yVLWFzMIpgTs~zBGgK9ltwAjsdkBhLhm6lzBZ2tV9ZPoxcseFbVrq6X~91u82VjDUyxxrpKHXhX7nUwAmBScsc2UHcMw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":4317,"name":"Nonlinear Optics","url":"https://www.academia.edu/Documents/in/Nonlinear_Optics"},{"id":118582,"name":"Physical sciences","url":"https://www.academia.edu/Documents/in/Physical_sciences"},{"id":260118,"name":"CHEMICAL SCIENCES","url":"https://www.academia.edu/Documents/in/CHEMICAL_SCIENCES"},{"id":482288,"name":"Binding Energy","url":"https://www.academia.edu/Documents/in/Binding_Energy"}],"urls":[]}, dispatcherData: dispatcherData }); 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The model is based on the bonding HOMO and LUMO states of the molecular repeat units. The model is numerically tractable in that it is solved for oligomers of up to 15 units using the density matrix renormalisation group method. The energy of the l'B,-exciton is in good agreement with experimental results for oligomers, and approaches ca. 2.7 eV for oligomers of 15 units. Likewise, we predict a 2'Ag+ exciton at ca. 2.8 eV, a l\"B,' exciton at 1.6 eV and the singlet exciton binding energy as being 1.4 eV for single chains. We extend this approach to target other absorption bands. 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We show theoretically that because of the close similarity of the singlet and triplet interchain wave functions, spin-orbit coupling between these states is negligible. Using density matrix renormalization group calculations on model systems, we confirm these theoretical predictions: spin-orbit coupling between interchain states is typically 103-104 times smaller than between corresponding intramolecular states, being typically ca. 1脳10-7eV for disordered polymers. 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We show theoretically that because of the close similarity of the singlet and triplet interchain wave functions, spin-orbit coupling between these states is negligible. Using density matrix renormalization group calculations on model systems, we confirm these theoretical predictions: spin-orbit coupling between interchain states is typically 103-104 times smaller than between corresponding intramolecular states, being typically ca. 1脳10-7eV for disordered polymers. We discuss the implication of these results for the possibly enhanced singlet exciton yield in light-emitting polymers.","publication_date":{"day":null,"month":null,"year":2010,"errors":{}},"publication_name":"Physical Review B Condensed Matter and Materials Physics"},"translated_abstract":"Motivated by the reported enhanced singlet exciton yield in light-emitting polymers, we investigate spin-orbit coupling between Coulombically bound interchain excitations. We show theoretically that because of the close similarity of the singlet and triplet interchain wave functions, spin-orbit coupling between these states is negligible. Using density matrix renormalization group calculations on model systems, we confirm these theoretical predictions: spin-orbit coupling between interchain states is typically 103-104 times smaller than between corresponding intramolecular states, being typically ca. 1脳10-7eV for disordered polymers. We discuss the implication of these results for the possibly enhanced singlet exciton yield in light-emitting polymers.","internal_url":"https://www.academia.edu/30208808/Spin_orbit_interactions_between_interchain_excitations_in_conjugated_polymers","translated_internal_url":"","created_at":"2016-12-01T17:26:34.406-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":57527093,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[{"id":26335112,"work_id":30208808,"tagging_user_id":57527093,"tagged_user_id":null,"co_author_invite_id":5809032,"email":"w***d@sheffield.ac.uk","display_order":0,"name":"William Barford","title":"Spin-orbit interactions between interchain excitations in conjugated polymers"},{"id":26335148,"work_id":30208808,"tagging_user_id":57527093,"tagged_user_id":null,"co_author_invite_id":3298809,"email":"d***v@leeds.ac.uk","display_order":4194304,"name":"Dmitry Makhov","title":"Spin-orbit interactions between interchain excitations in conjugated polymers"}],"downloadable_attachments":[],"slug":"Spin_orbit_interactions_between_interchain_excitations_in_conjugated_polymers","translated_slug":"","page_count":null,"language":"en","content_type":"Work","owner":{"id":57527093,"first_name":"Robert","middle_initials":null,"last_name":"Bursill","page_name":"RobertBursill","domain_name":"independent","created_at":"2016-12-01T17:26:12.952-08:00","display_name":"Robert Bursill","url":"https://independent.academia.edu/RobertBursill"},"attachments":[],"research_interests":[{"id":118582,"name":"Physical sciences","url":"https://www.academia.edu/Documents/in/Physical_sciences"},{"id":260118,"name":"CHEMICAL SCIENCES","url":"https://www.academia.edu/Documents/in/CHEMICAL_SCIENCES"},{"id":1735044,"name":"Spin Orbit Coupling","url":"https://www.academia.edu/Documents/in/Spin_Orbit_Coupling"}],"urls":[{"id":7786762,"url":"http://adsabs.harvard.edu/abs/2010phrvb..81c5206b"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="30208807"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/30208807/Erratum_to_density_matrix_renormalisation_group_calculations_of_molecular_exciton_energies_in_poly_phenylene_vinylene_synthetic_metals_85_1997_1155_"><img alt="Research paper thumbnail of Erratum to ?density matrix renormalisation group calculations of molecular exciton energies in poly (-phenylene vinylene)? [synthetic metals, 85 (1997) 1155]" class="work-thumbnail" src="https://attachments.academia-assets.com/50667475/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/30208807/Erratum_to_density_matrix_renormalisation_group_calculations_of_molecular_exciton_energies_in_poly_phenylene_vinylene_synthetic_metals_85_1997_1155_">Erratum to ?density matrix renormalisation group calculations of molecular exciton energies in poly (-phenylene vinylene)? 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="30208805"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/30208805/Excited_states_of_linear_polyenes"><img alt="Research paper thumbnail of Excited states of linear polyenes" class="work-thumbnail" src="https://attachments.academia-assets.com/50667439/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/30208805/Excited_states_of_linear_polyenes">Excited states of linear polyenes</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We present density matrix renormalisation group calculations of the Pariser- Parr-Pople-Peierls m...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We present density matrix renormalisation group calculations of the Pariser- Parr-Pople-Peierls model of linear polyenes within the adiabatic approximation. We calculate the vertical and relaxed transition energies, and relaxed geometries for various excitations on long chains. The triplet (3Bu+) and even- parity singlet (2Ag+) states have a 2-soliton and 4-soliton form, respectively, both with large relaxation energies. The dipole-allowed (1Bu-) state forms an exciton-polaron and has a very small relaxation energy. The relaxed energy of the 2Ag+ state lies below that of the 1Bu- state. We observe an attraction between the soliton-antisoliton pairs in the 2Ag+ state. The calculated excitation energies agree well with the observed values for polyene oligomers; the agreement with polyacetylene thin films is less good, and we comment on the possible sources of the discrepencies. The photoinduced absorption is interpreted. The spin-spin correlation function shows that the unpaired spins coincide with the geometrical soliton positions. We study the roles of electron-electron interactions and electron-lattice coupling in determining the excitation energies and soliton structures. The electronic interactions play the key role in determining the ground state dimerisation and the excited state transition energies.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="270ac5630e86d4eb8c2bcb79bfbb3d30" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":50667439,"asset_id":30208805,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/50667439/download_file?st=MTczMjQ1MjAxNyw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="30208805"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="30208805"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 30208805; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=30208805]").text(description); $(".js-view-count[data-work-id=30208805]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 30208805; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='30208805']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 30208805, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "270ac5630e86d4eb8c2bcb79bfbb3d30" } } $('.js-work-strip[data-work-id=30208805]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":30208805,"title":"Excited states of linear polyenes","translated_title":"","metadata":{"abstract":"We present density matrix renormalisation group calculations of the Pariser- Parr-Pople-Peierls model of linear polyenes within the adiabatic approximation. We calculate the vertical and relaxed transition energies, and relaxed geometries for various excitations on long chains. The triplet (3Bu+) and even- parity singlet (2Ag+) states have a 2-soliton and 4-soliton form, respectively, both with large relaxation energies. The dipole-allowed (1Bu-) state forms an exciton-polaron and has a very small relaxation energy. The relaxed energy of the 2Ag+ state lies below that of the 1Bu- state. We observe an attraction between the soliton-antisoliton pairs in the 2Ag+ state. The calculated excitation energies agree well with the observed values for polyene oligomers; the agreement with polyacetylene thin films is less good, and we comment on the possible sources of the discrepencies. The photoinduced absorption is interpreted. The spin-spin correlation function shows that the unpaired spins coincide with the geometrical soliton positions. We study the roles of electron-electron interactions and electron-lattice coupling in determining the excitation energies and soliton structures. The electronic interactions play the key role in determining the ground state dimerisation and the excited state transition energies.","publication_date":{"day":5,"month":3,"year":2001,"errors":{}}},"translated_abstract":"We present density matrix renormalisation group calculations of the Pariser- Parr-Pople-Peierls model of linear polyenes within the adiabatic approximation. We calculate the vertical and relaxed transition energies, and relaxed geometries for various excitations on long chains. The triplet (3Bu+) and even- parity singlet (2Ag+) states have a 2-soliton and 4-soliton form, respectively, both with large relaxation energies. The dipole-allowed (1Bu-) state forms an exciton-polaron and has a very small relaxation energy. The relaxed energy of the 2Ag+ state lies below that of the 1Bu- state. We observe an attraction between the soliton-antisoliton pairs in the 2Ag+ state. The calculated excitation energies agree well with the observed values for polyene oligomers; the agreement with polyacetylene thin films is less good, and we comment on the possible sources of the discrepencies. The photoinduced absorption is interpreted. The spin-spin correlation function shows that the unpaired spins coincide with the geometrical soliton positions. We study the roles of electron-electron interactions and electron-lattice coupling in determining the excitation energies and soliton structures. The electronic interactions play the key role in determining the ground state dimerisation and the excited state transition energies.","internal_url":"https://www.academia.edu/30208805/Excited_states_of_linear_polyenes","translated_internal_url":"","created_at":"2016-12-01T17:26:33.933-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":57527093,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[{"id":26335085,"work_id":30208805,"tagging_user_id":57527093,"tagged_user_id":null,"co_author_invite_id":5809031,"email":"m***v@bristol.ac.uk","display_order":0,"name":"Mikhail Lavrentiev","title":"Excited states of linear polyenes"},{"id":26335116,"work_id":30208805,"tagging_user_id":57527093,"tagged_user_id":null,"co_author_invite_id":5809032,"email":"w***d@sheffield.ac.uk","display_order":4194304,"name":"William Barford","title":"Excited states of linear polyenes"}],"downloadable_attachments":[{"id":50667439,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/50667439/thumbnails/1.jpg","file_name":"0103100.pdf","download_url":"https://www.academia.edu/attachments/50667439/download_file?st=MTczMjQ1MjAxNyw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Excited_states_of_linear_polyenes.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/50667439/0103100-libre.pdf?1480642671=\u0026response-content-disposition=attachment%3B+filename%3DExcited_states_of_linear_polyenes.pdf\u0026Expires=1732455617\u0026Signature=XUIMvJ2sJVZHW5LTTKOzXT28xmLudOEVD91xmrartSRKnoDpATRipYvugFR-JEoa~daEq9sdadH4ikiivQqAkChTT2syOYEim0~998gm1eFoUozmncS4rx8sXTyWnQjLWBaiwvUPPBSkiAtDiOl5HGKqFk5O~9u0kVEPW2UP2hu7uSsROjmVtMa5hqbgqljmELns~iOBPn-ukpwf2ur-BTNiAmxR7uvDrd573Jbex7ZbhIgtgNWGyoehL4mFFeLWTrQ8vvewnOPt6b0MvWUO-5tKKYqUSVN0dhEJPFK7cH2G9ohLs4mbjWAt-c9ao-4G7IFkHjsX8HdVPH0w6C8dFQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Excited_states_of_linear_polyenes","translated_slug":"","page_count":23,"language":"en","content_type":"Work","owner":{"id":57527093,"first_name":"Robert","middle_initials":null,"last_name":"Bursill","page_name":"RobertBursill","domain_name":"independent","created_at":"2016-12-01T17:26:12.952-08:00","display_name":"Robert Bursill","url":"https://independent.academia.edu/RobertBursill"},"attachments":[{"id":50667439,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/50667439/thumbnails/1.jpg","file_name":"0103100.pdf","download_url":"https://www.academia.edu/attachments/50667439/download_file?st=MTczMjQ1MjAxNyw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Excited_states_of_linear_polyenes.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/50667439/0103100-libre.pdf?1480642671=\u0026response-content-disposition=attachment%3B+filename%3DExcited_states_of_linear_polyenes.pdf\u0026Expires=1732455617\u0026Signature=XUIMvJ2sJVZHW5LTTKOzXT28xmLudOEVD91xmrartSRKnoDpATRipYvugFR-JEoa~daEq9sdadH4ikiivQqAkChTT2syOYEim0~998gm1eFoUozmncS4rx8sXTyWnQjLWBaiwvUPPBSkiAtDiOl5HGKqFk5O~9u0kVEPW2UP2hu7uSsROjmVtMa5hqbgqljmELns~iOBPn-ukpwf2ur-BTNiAmxR7uvDrd573Jbex7ZbhIgtgNWGyoehL4mFFeLWTrQ8vvewnOPt6b0MvWUO-5tKKYqUSVN0dhEJPFK7cH2G9ohLs4mbjWAt-c9ao-4G7IFkHjsX8HdVPH0w6C8dFQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"},{"id":50667438,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/50667438/thumbnails/1.jpg","file_name":"0103100.pdf","download_url":"https://www.academia.edu/attachments/50667438/download_file","bulk_download_file_name":"Excited_states_of_linear_polyenes.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/50667438/0103100-libre.pdf?1480642672=\u0026response-content-disposition=attachment%3B+filename%3DExcited_states_of_linear_polyenes.pdf\u0026Expires=1732455617\u0026Signature=R3pPgGr2jiJcw~TkaWmC4nR9VA5ySxKCGX52sfp3Z~92B6les9KoGM4Q3IuUFDG9pPwgfMMJs9UI8Z0ItNYK8aEQnkNQ9Lv4ly2wn9zJi1QiSLieB1dv2LuT-aoj8yf4XA6IMlk1nkx-2Nolc0FcMO3FhlOgNp~1dtVxf8~CaZoKv-0bSLrjSr88V2Mn1dj19VwuD3w4jfYNgQW0Hukr1tt6ddsSjf6wBOJe9pvT~iGJtmTAShyTuz0NV-jVH2TigPR9Hf5ywzU7NWAA~m8lq0qxtbjIcqbMJz3jRce5zEknZVtfqBMUKQPvNzUpUyH1SdRCINo8ERUVjQl3e~Ofcw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":101573,"name":"Thin Film","url":"https://www.academia.edu/Documents/in/Thin_Film"},{"id":393410,"name":"Excited states","url":"https://www.academia.edu/Documents/in/Excited_states"},{"id":435600,"name":"Density Matrix","url":"https://www.academia.edu/Documents/in/Density_Matrix"},{"id":2382100,"name":"Correlation function","url":"https://www.academia.edu/Documents/in/Correlation_function"}],"urls":[{"id":7786760,"url":"http://arxiv.org/abs/cond-mat/0103100"}]}, dispatcherData: dispatcherData }); 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Samaras","title":"Green's Function Monte Carlo Approach to Su (3) Yang-Mills Theory in (3+1) D"}],"downloadable_attachments":[{"id":50667477,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/50667477/thumbnails/1.jpg","file_name":"Greens_Function_Monte_Carlo_approach_to20161201-11383-1syuse.pdf","download_url":"https://www.academia.edu/attachments/50667477/download_file?st=MTczMjQ1MjAxOCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Greens_Function_Monte_Carlo_Approach_to.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/50667477/Greens_Function_Monte_Carlo_approach_to20161201-11383-1syuse-libre.pdf?1480642650=\u0026response-content-disposition=attachment%3B+filename%3DGreens_Function_Monte_Carlo_Approach_to.pdf\u0026Expires=1732455618\u0026Signature=dW4zv9HHotOR7I0DHr5Ao4LTxkXTxknyZ8nJdisgeEtgK2CycaOeucc~tEu0ae8YdGhauR1D3GmXRSoVjP18xKcow74jG5BB9VmdjcmFJo9XpIn2SwoD8VJfll6r7vH7qtI7krzy0szqhsGItHY8Qdq3adCiREUPR8EW3ZXeMMWIk0QY6PVzsVzZ4DmxWTWe5x7SX-n10Z7z~tlZcCoBjWFC5u4de02EP2dxqCyCqzOufIUbN6dk~5DzLlc185ncY2Nbo8aSV21CsZF7mY9A1FdymbdzievHWzG9flbEpoXmVJlbwn788PiUYaqOcc2jxbNv-CYSFeEBaD~NsGB93Q__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Greens_Function_Monte_Carlo_Approach_to_Su_3_Yang_Mills_Theory_in_3_1_D","translated_slug":"","page_count":10,"language":"en","content_type":"Work","owner":{"id":57527093,"first_name":"Robert","middle_initials":null,"last_name":"Bursill","page_name":"RobertBursill","domain_name":"independent","created_at":"2016-12-01T17:26:12.952-08:00","display_name":"Robert Bursill","url":"https://independent.academia.edu/RobertBursill"},"attachments":[{"id":50667477,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/50667477/thumbnails/1.jpg","file_name":"Greens_Function_Monte_Carlo_approach_to20161201-11383-1syuse.pdf","download_url":"https://www.academia.edu/attachments/50667477/download_file?st=MTczMjQ1MjAxOCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Greens_Function_Monte_Carlo_Approach_to.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/50667477/Greens_Function_Monte_Carlo_approach_to20161201-11383-1syuse-libre.pdf?1480642650=\u0026response-content-disposition=attachment%3B+filename%3DGreens_Function_Monte_Carlo_Approach_to.pdf\u0026Expires=1732455618\u0026Signature=dW4zv9HHotOR7I0DHr5Ao4LTxkXTxknyZ8nJdisgeEtgK2CycaOeucc~tEu0ae8YdGhauR1D3GmXRSoVjP18xKcow74jG5BB9VmdjcmFJo9XpIn2SwoD8VJfll6r7vH7qtI7krzy0szqhsGItHY8Qdq3adCiREUPR8EW3ZXeMMWIk0QY6PVzsVzZ4DmxWTWe5x7SX-n10Z7z~tlZcCoBjWFC5u4de02EP2dxqCyCqzOufIUbN6dk~5DzLlc185ncY2Nbo8aSV21CsZF7mY9A1FdymbdzievHWzG9flbEpoXmVJlbwn788PiUYaqOcc2jxbNv-CYSFeEBaD~NsGB93Q__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="30208800"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/30208800/Persistent_currents_in_the_Heisenberg_chain_with_a_weak_link"><img alt="Research paper thumbnail of Persistent currents in the Heisenberg chain with a weak link" class="work-thumbnail" src="https://attachments.academia-assets.com/50667472/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/30208800/Persistent_currents_in_the_Heisenberg_chain_with_a_weak_link">Persistent currents in the Heisenberg chain with a weak link</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://independent.academia.edu/RobertBursill">Robert Bursill</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://neural.academia.edu/HansPeterEckle">Hans-Peter Eckle</a></span></div><div class="wp-workCard_item"><span>Physical Review B</span><span>, 2002</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="b9b7d196cdce36c3796bdcd7bfd9e7a3" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":50667472,"asset_id":30208800,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/50667472/download_file?st=MTczMjQ1MjAxOCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="30208800"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="30208800"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 30208800; 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The Heisenberg chain is equivalent to a spinless electron gas under a Jordan-Wigner transformation. Using density matrix renormalization group and quantum Monte Carlo methods we calculate the spin/charge stiffness of the model, which determines the strength of the 'persistent currents'. The stiffness is found to scale to zero in the weak link case, in agreement with renormalization group arguments of Eggert and Affleck, and Kane and Fisher.","publication_date":{"day":null,"month":null,"year":2002,"errors":{}},"publication_name":"Physical Review B","grobid_abstract_attachment_id":50667472},"translated_abstract":null,"internal_url":"https://www.academia.edu/30208800/Persistent_currents_in_the_Heisenberg_chain_with_a_weak_link","translated_internal_url":"","created_at":"2016-12-01T17:26:33.137-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":57527093,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[{"id":26335070,"work_id":30208800,"tagging_user_id":57527093,"tagged_user_id":null,"co_author_invite_id":5809029,"email":"c***2@student.monash.edu","display_order":0,"name":"Christopher Hamer","title":"Persistent currents in the Heisenberg chain with a weak link"},{"id":26335154,"work_id":30208800,"tagging_user_id":57527093,"tagged_user_id":null,"co_author_invite_id":2989099,"email":"s***k@buphy.bu.edu","display_order":4194304,"name":"Anders Sandvik","title":"Persistent currents in the Heisenberg chain with a weak link"},{"id":26335263,"work_id":30208800,"tagging_user_id":57527093,"tagged_user_id":42137443,"co_author_invite_id":null,"email":"t***s@colgate.edu","affiliation":"Colgate University","display_order":6291456,"name":"Timothy Byrnes","title":"Persistent currents in the Heisenberg chain with a weak link"},{"id":26335265,"work_id":30208800,"tagging_user_id":57527093,"tagged_user_id":16555052,"co_author_invite_id":null,"email":"h***e@googlemail.com","affiliation":"University of Ulm","display_order":7340032,"name":"Hans-Peter Eckle","title":"Persistent currents in the Heisenberg chain with a weak link"}],"downloadable_attachments":[{"id":50667472,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/50667472/thumbnails/1.jpg","file_name":"0deec519f79bf90952000000.pdf","download_url":"https://www.academia.edu/attachments/50667472/download_file?st=MTczMjQ1MjAxOCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Persistent_currents_in_the_Heisenberg_ch.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/50667472/0deec519f79bf90952000000-libre.pdf?1480642654=\u0026response-content-disposition=attachment%3B+filename%3DPersistent_currents_in_the_Heisenberg_ch.pdf\u0026Expires=1732455618\u0026Signature=I5X1beTC5jCK~Fsf4QeB7ckMoxlPZr-1q1949Kk1LYx71bkWF8QjxUXhhkVZZGK7qENHdiO9aXjY1Z0Kw0bTwPOjeOV1xi~s2yc9GJbxxrGolLgt0GQpk9Ys4~1Wfk1CiAmsvh2vVJOo83XaTdHbddU7lzJMPgArNzxnbF2jRcLNMyQbqpKwGQYFaaZk~ZLWV15lhiyJXOWjkA5IGqJeklRGLjr~H~bRLqqFmq1DBSP-~a2xWVe2ekLQpWFy-cIfqXToze2l6AtlyycepMpuykbOOUW9Khs~LMhwbBHkgI~ID0UCCAP9G4rXeQFBuTnHKj~UNxBRiiZJ30ScWbkE0A__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Persistent_currents_in_the_Heisenberg_chain_with_a_weak_link","translated_slug":"","page_count":15,"language":"en","content_type":"Work","owner":{"id":57527093,"first_name":"Robert","middle_initials":null,"last_name":"Bursill","page_name":"RobertBursill","domain_name":"independent","created_at":"2016-12-01T17:26:12.952-08:00","display_name":"Robert Bursill","url":"https://independent.academia.edu/RobertBursill"},"attachments":[{"id":50667472,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/50667472/thumbnails/1.jpg","file_name":"0deec519f79bf90952000000.pdf","download_url":"https://www.academia.edu/attachments/50667472/download_file?st=MTczMjQ1MjAxOCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Persistent_currents_in_the_Heisenberg_ch.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/50667472/0deec519f79bf90952000000-libre.pdf?1480642654=\u0026response-content-disposition=attachment%3B+filename%3DPersistent_currents_in_the_Heisenberg_ch.pdf\u0026Expires=1732455618\u0026Signature=I5X1beTC5jCK~Fsf4QeB7ckMoxlPZr-1q1949Kk1LYx71bkWF8QjxUXhhkVZZGK7qENHdiO9aXjY1Z0Kw0bTwPOjeOV1xi~s2yc9GJbxxrGolLgt0GQpk9Ys4~1Wfk1CiAmsvh2vVJOo83XaTdHbddU7lzJMPgArNzxnbF2jRcLNMyQbqpKwGQYFaaZk~ZLWV15lhiyJXOWjkA5IGqJeklRGLjr~H~bRLqqFmq1DBSP-~a2xWVe2ekLQpWFy-cIfqXToze2l6AtlyycepMpuykbOOUW9Khs~LMhwbBHkgI~ID0UCCAP9G4rXeQFBuTnHKj~UNxBRiiZJ30ScWbkE0A__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":14272,"name":"Quantum Monte Carlo","url":"https://www.academia.edu/Documents/in/Quantum_Monte_Carlo"},{"id":494966,"name":"Renormalization Group","url":"https://www.academia.edu/Documents/in/Renormalization_Group"},{"id":519863,"name":"Persistent Current","url":"https://www.academia.edu/Documents/in/Persistent_Current"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="30208799"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/30208799/Quantized_Lattice_Dynamic_Effects_on_the_Spin_Peierls_Transition"><img alt="Research paper thumbnail of Quantized Lattice Dynamic Effects on the Spin-Peierls Transition" class="work-thumbnail" src="https://attachments.academia-assets.com/50667470/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/30208799/Quantized_Lattice_Dynamic_Effects_on_the_Spin_Peierls_Transition">Quantized Lattice Dynamic Effects on the Spin-Peierls Transition</a></div><div class="wp-workCard_item"><span>Physical Review B Condensed Matter and Materials Physics</span><span>, Jul 22, 2010</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The density-matrix renormalization-group method is used to investigate the spin-Peierls transitio...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The density-matrix renormalization-group method is used to investigate the spin-Peierls transition for Heisenberg spins coupled to quantized phonons. We use a phonon spectrum that interpolates between a gapped, dispersionless (Einstein) limit to a gapless, dispersive (Debye) limit. A variety of theoretical probes are used to determine the quantum phase transition, including energy gap crossing, a finite-size scaling analysis, bond-order autocorrelation functions, and bipartite quantum entanglement. All these probes indicate that in the antiadiabatic phonon limit a quantum phase transition of the Berezinskii-Kosterlitz-Thouless type is observed at a nonzero spin-phonon coupling, gc . An extrapolation from the Einstein limit to the Debye limit is accompanied by an increase in gc for a fixed optical (q=蟺) phonon gap. We therefore conclude that the dimerized ground state is more unstable with respect to Debye phonons with the introduction of phonon-dispersion renormalizing the effective spin-lattice coupling for the Peierls-active mode. We also show that the staggered spin-spin and phonon displacement order parameters are unreliable means of determining the transition.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="51d89e31ac14041056e1ea07ca3a1c81" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":50667470,"asset_id":30208799,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/50667470/download_file?st=MTczMjQ1MjAxOCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="30208799"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="30208799"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 30208799; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=30208799]").text(description); $(".js-view-count[data-work-id=30208799]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 30208799; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='30208799']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 30208799, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "51d89e31ac14041056e1ea07ca3a1c81" } } $('.js-work-strip[data-work-id=30208799]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":30208799,"title":"Quantized Lattice Dynamic Effects on the Spin-Peierls Transition","translated_title":"","metadata":{"abstract":"The density-matrix renormalization-group method is used to investigate the spin-Peierls transition for Heisenberg spins coupled to quantized phonons. We use a phonon spectrum that interpolates between a gapped, dispersionless (Einstein) limit to a gapless, dispersive (Debye) limit. A variety of theoretical probes are used to determine the quantum phase transition, including energy gap crossing, a finite-size scaling analysis, bond-order autocorrelation functions, and bipartite quantum entanglement. All these probes indicate that in the antiadiabatic phonon limit a quantum phase transition of the Berezinskii-Kosterlitz-Thouless type is observed at a nonzero spin-phonon coupling, gc . An extrapolation from the Einstein limit to the Debye limit is accompanied by an increase in gc for a fixed optical (q=蟺) phonon gap. We therefore conclude that the dimerized ground state is more unstable with respect to Debye phonons with the introduction of phonon-dispersion renormalizing the effective spin-lattice coupling for the Peierls-active mode. We also show that the staggered spin-spin and phonon displacement order parameters are unreliable means of determining the transition.","publication_date":{"day":22,"month":7,"year":2010,"errors":{}},"publication_name":"Physical Review B Condensed Matter and Materials Physics"},"translated_abstract":"The density-matrix renormalization-group method is used to investigate the spin-Peierls transition for Heisenberg spins coupled to quantized phonons. We use a phonon spectrum that interpolates between a gapped, dispersionless (Einstein) limit to a gapless, dispersive (Debye) limit. A variety of theoretical probes are used to determine the quantum phase transition, including energy gap crossing, a finite-size scaling analysis, bond-order autocorrelation functions, and bipartite quantum entanglement. All these probes indicate that in the antiadiabatic phonon limit a quantum phase transition of the Berezinskii-Kosterlitz-Thouless type is observed at a nonzero spin-phonon coupling, gc . An extrapolation from the Einstein limit to the Debye limit is accompanied by an increase in gc for a fixed optical (q=蟺) phonon gap. We therefore conclude that the dimerized ground state is more unstable with respect to Debye phonons with the introduction of phonon-dispersion renormalizing the effective spin-lattice coupling for the Peierls-active mode. We also show that the staggered spin-spin and phonon displacement order parameters are unreliable means of determining the transition.","internal_url":"https://www.academia.edu/30208799/Quantized_Lattice_Dynamic_Effects_on_the_Spin_Peierls_Transition","translated_internal_url":"","created_at":"2016-12-01T17:26:32.954-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":57527093,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[{"id":26335114,"work_id":30208799,"tagging_user_id":57527093,"tagged_user_id":null,"co_author_invite_id":5809032,"email":"w***d@sheffield.ac.uk","display_order":0,"name":"William Barford","title":"Quantized Lattice Dynamic Effects on the Spin-Peierls Transition"},{"id":26335132,"work_id":30208799,"tagging_user_id":57527093,"tagged_user_id":null,"co_author_invite_id":5809038,"email":"c***n@internode.on.net","display_order":4194304,"name":"Christopher Pearson","title":"Quantized Lattice Dynamic Effects on the Spin-Peierls Transition"}],"downloadable_attachments":[{"id":50667470,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/50667470/thumbnails/1.jpg","file_name":"1007.3860.pdf","download_url":"https://www.academia.edu/attachments/50667470/download_file?st=MTczMjQ1MjAxOCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Quantized_Lattice_Dynamic_Effects_on_the.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/50667470/1007.3860-libre.pdf?1480642658=\u0026response-content-disposition=attachment%3B+filename%3DQuantized_Lattice_Dynamic_Effects_on_the.pdf\u0026Expires=1732455618\u0026Signature=gCNFhEz1rEcAydafQvL6mx43oeC8u8OTC6ElfBqTaJaBsu3-Kb5otH~nZWtsHgFMhKP2yc~t6ZJVxrbaFiUlCXndN75NN78gqzceDC3JhwZ9xDYPemPJcHWuinldh3-ecKifUrRAvUWwW-HqvDGTXtG194z1fjIHC6eLXYzgpd3briSmGLO--e3FTO2XKyAZNabUHPogeSTIH~Q01ylZVF94MRgowJ9FXsSVVaw9nigr5iXKIODrPIfmtCo6CLpQ79tal3x005nL8kgFvW3OqaF00bP20OGggKtZlKfiHGuV4NroFa2H7yOT8waq6AswSJIIgZqG4KNKIWXaiJrBfg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Quantized_Lattice_Dynamic_Effects_on_the_Spin_Peierls_Transition","translated_slug":"","page_count":24,"language":"en","content_type":"Work","owner":{"id":57527093,"first_name":"Robert","middle_initials":null,"last_name":"Bursill","page_name":"RobertBursill","domain_name":"independent","created_at":"2016-12-01T17:26:12.952-08:00","display_name":"Robert Bursill","url":"https://independent.academia.edu/RobertBursill"},"attachments":[{"id":50667470,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/50667470/thumbnails/1.jpg","file_name":"1007.3860.pdf","download_url":"https://www.academia.edu/attachments/50667470/download_file?st=MTczMjQ1MjAxOCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Quantized_Lattice_Dynamic_Effects_on_the.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/50667470/1007.3860-libre.pdf?1480642658=\u0026response-content-disposition=attachment%3B+filename%3DQuantized_Lattice_Dynamic_Effects_on_the.pdf\u0026Expires=1732455618\u0026Signature=gCNFhEz1rEcAydafQvL6mx43oeC8u8OTC6ElfBqTaJaBsu3-Kb5otH~nZWtsHgFMhKP2yc~t6ZJVxrbaFiUlCXndN75NN78gqzceDC3JhwZ9xDYPemPJcHWuinldh3-ecKifUrRAvUWwW-HqvDGTXtG194z1fjIHC6eLXYzgpd3briSmGLO--e3FTO2XKyAZNabUHPogeSTIH~Q01ylZVF94MRgowJ9FXsSVVaw9nigr5iXKIODrPIfmtCo6CLpQ79tal3x005nL8kgFvW3OqaF00bP20OGggKtZlKfiHGuV4NroFa2H7yOT8waq6AswSJIIgZqG4KNKIWXaiJrBfg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":43591,"name":"Quantum entanglement","url":"https://www.academia.edu/Documents/in/Quantum_entanglement"},{"id":118582,"name":"Physical sciences","url":"https://www.academia.edu/Documents/in/Physical_sciences"},{"id":260118,"name":"CHEMICAL SCIENCES","url":"https://www.academia.edu/Documents/in/CHEMICAL_SCIENCES"},{"id":321836,"name":"Spectrum","url":"https://www.academia.edu/Documents/in/Spectrum"},{"id":983074,"name":"Quantum Phase Transition","url":"https://www.academia.edu/Documents/in/Quantum_Phase_Transition"},{"id":1118571,"name":"Autocorrelation Function","url":"https://www.academia.edu/Documents/in/Autocorrelation_Function"}],"urls":[{"id":7786756,"url":"http://adsabs.harvard.edu/abs/2010PhRvB..82n4408P"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> </div><div class="profile--tab_content_container js-tab-pane tab-pane" data-section-id="6239670" id="papers"><div class="js-work-strip profile--work_container" data-work-id="30269806"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/30269806/A_density_matrix_renormalisation_group_algorithm_for_quantum_lattice_systems_with_a_large_number_of_states_per_site"><img alt="Research paper thumbnail of A density matrix renormalisation group algorithm for quantum lattice systems with a large number of states per site" class="work-thumbnail" src="https://attachments.academia-assets.com/50736768/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/30269806/A_density_matrix_renormalisation_group_algorithm_for_quantum_lattice_systems_with_a_large_number_of_states_per_site">A density matrix renormalisation group algorithm for quantum lattice systems with a large number of states per site</a></div><div class="wp-workCard_item"><span>Phys Rev B</span><span>, 1999</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">A variant of White's density matrix renormalisation group scheme which is designed to compute low...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">A variant of White's density matrix renormalisation group scheme which is designed to compute low-lying energies of one-dimensional quantum lattice models with a large number of degrees of freedom per site is described. The method is tested on two exactly solvable models---the spin-1/2 antiferromagnetic Heisenberg chain and a dimerised XY spin chain. To illustrate the potential of the method, it is applied to a model of spins interacting with quantum phonons. It is shown that the method accurately resolves a number of energy gaps on periodic rings which are sufficiently large to afford an accurate investigation of critical properties via the use of finite-size scaling theory.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="b285159a5ffc066b0bcf694aae174ede" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":50736768,"asset_id":30269806,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/50736768/download_file?st=MTczMjQ1MjAxOCw4LjIyMi4yMDguMTQ2&st=MTczMjQ1MjAxNyw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="30269806"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="30269806"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 30269806; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=30269806]").text(description); $(".js-view-count[data-work-id=30269806]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 30269806; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='30269806']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 30269806, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "b285159a5ffc066b0bcf694aae174ede" } } $('.js-work-strip[data-work-id=30269806]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":30269806,"title":"A density matrix renormalisation group algorithm for quantum lattice systems with a large number of states per site","translated_title":"","metadata":{"abstract":"A variant of White's density matrix renormalisation group scheme which is designed to compute low-lying energies of one-dimensional quantum lattice models with a large number of degrees of freedom per site is described. The method is tested on two exactly solvable models---the spin-1/2 antiferromagnetic Heisenberg chain and a dimerised XY spin chain. To illustrate the potential of the method, it is applied to a model of spins interacting with quantum phonons. It is shown that the method accurately resolves a number of energy gaps on periodic rings which are sufficiently large to afford an accurate investigation of critical properties via the use of finite-size scaling theory.","publication_date":{"day":null,"month":null,"year":1999,"errors":{}},"publication_name":"Phys Rev B"},"translated_abstract":"A variant of White's density matrix renormalisation group scheme which is designed to compute low-lying energies of one-dimensional quantum lattice models with a large number of degrees of freedom per site is described. The method is tested on two exactly solvable models---the spin-1/2 antiferromagnetic Heisenberg chain and a dimerised XY spin chain. To illustrate the potential of the method, it is applied to a model of spins interacting with quantum phonons. It is shown that the method accurately resolves a number of energy gaps on periodic rings which are sufficiently large to afford an accurate investigation of critical properties via the use of finite-size scaling theory.","internal_url":"https://www.academia.edu/30269806/A_density_matrix_renormalisation_group_algorithm_for_quantum_lattice_systems_with_a_large_number_of_states_per_site","translated_internal_url":"","created_at":"2016-12-05T23:12:54.539-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":57527093,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":50736768,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/50736768/thumbnails/1.jpg","file_name":"9812349.pdf","download_url":"https://www.academia.edu/attachments/50736768/download_file?st=MTczMjQ1MjAxOCw4LjIyMi4yMDguMTQ2&st=MTczMjQ1MjAxNyw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"A_density_matrix_renormalisation_group_a.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/50736768/9812349-libre.pdf?1481008604=\u0026response-content-disposition=attachment%3B+filename%3DA_density_matrix_renormalisation_group_a.pdf\u0026Expires=1732455617\u0026Signature=LW4~zYyrsVRNzIvDsGtbMVpd58zZ5Gph0TsVPfQJRaQrWOf4X-Y9Ymf4p3dANw1piDMle8ATO8mcxdwyxIGMMfR7pAyRZ8-1ylhl46mcz49lH-sNdMPEGIASAGltCLRDoZ1KJBwTtLAth5AWubp4Ghu9q3Qz59uzZrxE~tfZyNBhomRzXEVH7vFZGQbkzsxXZ0Uc~YvS1vTd35DvHuz38NgN~wK4-oA9NeADbzRmefSDUA3R4mrBpW6Lj5MlEoa2JzMEVxkDSNYZKqm8wwhPgE2rkkgqUSkFHo2bQy3Rgb8akyevcHOWwIxTP9yqzd6fPTT-zShgF60grfXZnT6McA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"A_density_matrix_renormalisation_group_algorithm_for_quantum_lattice_systems_with_a_large_number_of_states_per_site","translated_slug":"","page_count":8,"language":"en","content_type":"Work","owner":{"id":57527093,"first_name":"Robert","middle_initials":null,"last_name":"Bursill","page_name":"RobertBursill","domain_name":"independent","created_at":"2016-12-01T17:26:12.952-08:00","display_name":"Robert Bursill","url":"https://independent.academia.edu/RobertBursill"},"attachments":[{"id":50736768,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/50736768/thumbnails/1.jpg","file_name":"9812349.pdf","download_url":"https://www.academia.edu/attachments/50736768/download_file?st=MTczMjQ1MjAxOCw4LjIyMi4yMDguMTQ2&st=MTczMjQ1MjAxNyw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"A_density_matrix_renormalisation_group_a.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/50736768/9812349-libre.pdf?1481008604=\u0026response-content-disposition=attachment%3B+filename%3DA_density_matrix_renormalisation_group_a.pdf\u0026Expires=1732455617\u0026Signature=LW4~zYyrsVRNzIvDsGtbMVpd58zZ5Gph0TsVPfQJRaQrWOf4X-Y9Ymf4p3dANw1piDMle8ATO8mcxdwyxIGMMfR7pAyRZ8-1ylhl46mcz49lH-sNdMPEGIASAGltCLRDoZ1KJBwTtLAth5AWubp4Ghu9q3Qz59uzZrxE~tfZyNBhomRzXEVH7vFZGQbkzsxXZ0Uc~YvS1vTd35DvHuz38NgN~wK4-oA9NeADbzRmefSDUA3R4mrBpW6Lj5MlEoa2JzMEVxkDSNYZKqm8wwhPgE2rkkgqUSkFHo2bQy3Rgb8akyevcHOWwIxTP9yqzd6fPTT-zShgF60grfXZnT6McA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"},{"id":50736769,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/50736769/thumbnails/1.jpg","file_name":"9812349.pdf","download_url":"https://www.academia.edu/attachments/50736769/download_file","bulk_download_file_name":"A_density_matrix_renormalisation_group_a.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/50736769/9812349-libre.pdf?1481008605=\u0026response-content-disposition=attachment%3B+filename%3DA_density_matrix_renormalisation_group_a.pdf\u0026Expires=1732455617\u0026Signature=Isfp5TH-t8nBjRA1Dlu-H2Ev-TRsNoS3z6GhbClfrecTC9zL6rER5tj3~5YlJiv0LneXWwFM0zU40aVQzh37bFc5s24EEajXwB5rWFiXjEeNgll8z97VRlNxDB9IxORM7QXM27tuR4s2ratLU1jhqbr8uyJfnSZO4Pvke24nk8Bu46pZk8EVXW9hD9z4cLZo9f-37r3Zz7H4Sjqg8EbglPO4KXiQup3WGFSlRXmdlt-3YpBg2HROq~8nARyyf9WqhMR5NkZLPXN1WtsoQWBvUBD47yQxbvYjth~2AhE4YWCvhiRG87QdQ8jq-V5WR2khCP8~XUkQl6ZAUC~HbNX~jg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":95016,"name":"Lattice Beam Model","url":"https://www.academia.edu/Documents/in/Lattice_Beam_Model"},{"id":435600,"name":"Density Matrix","url":"https://www.academia.edu/Documents/in/Density_Matrix"},{"id":767164,"name":"Spin Chain","url":"https://www.academia.edu/Documents/in/Spin_Chain"},{"id":1242198,"name":"Degree of Freedom","url":"https://www.academia.edu/Documents/in/Degree_of_Freedom"},{"id":1495455,"name":"Finite Size Scaling","url":"https://www.academia.edu/Documents/in/Finite_Size_Scaling"}],"urls":[{"id":7794361,"url":"http://arxiv.org/abs/cond-mat/9812349"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="30269805"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/30269805/One_dimensional_continuum_Falicov_Kimball_model_in_the_strongly_correlated_limit"><img alt="Research paper thumbnail of One dimensional continuum Falicov-Kimball model in the strongly correlated limit" class="work-thumbnail" src="https://attachments.academia-assets.com/50736787/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/30269805/One_dimensional_continuum_Falicov_Kimball_model_in_the_strongly_correlated_limit">One dimensional continuum Falicov-Kimball model in the strongly correlated limit</a></div><div class="wp-workCard_item"><span>Physica A: Statistical Mechanics and its Applications</span><span>, 1994</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="fb650ed486f12056598f2abca8333f07" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":50736787,"asset_id":30269805,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/50736787/download_file?st=MTczMjQ1MjAxOCw4LjIyMi4yMDguMTQ2&st=MTczMjQ1MjAxNyw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="30269805"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="30269805"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 30269805; 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In the ground state it is found that the f electrons form a cluster. 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The model is based on the bonding HOMO and LUMO states of the molecular repeat units. The model is numerically tractable in that it is solved for oligomers of up to 15 units using the density matrix renormalisation group method. The energy of the l'B,-exciton is in good agreement with experimental results for oligomers, and approaches ca. 2.7 eV for oligomers of 15 units. Likewise, we predict a 2'Ag+ exciton at ca. 2.8 eV, a l\"B,' exciton at 1.6 eV and the singlet exciton binding energy as being 1.4 eV for single chains. We extend this approach to target other absorption bands. 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We show theoretically that because of the close similarity of the singlet and triplet interchain wave functions, spin-orbit coupling between these states is negligible. Using density matrix renormalization group calculations on model systems, we confirm these theoretical predictions: spin-orbit coupling between interchain states is typically 103-104 times smaller than between corresponding intramolecular states, being typically ca. 1脳10-7eV for disordered polymers. 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We show theoretically that because of the close similarity of the singlet and triplet interchain wave functions, spin-orbit coupling between these states is negligible. Using density matrix renormalization group calculations on model systems, we confirm these theoretical predictions: spin-orbit coupling between interchain states is typically 103-104 times smaller than between corresponding intramolecular states, being typically ca. 1脳10-7eV for disordered polymers. We discuss the implication of these results for the possibly enhanced singlet exciton yield in light-emitting polymers.","publication_date":{"day":null,"month":null,"year":2010,"errors":{}},"publication_name":"Physical Review B Condensed Matter and Materials Physics"},"translated_abstract":"Motivated by the reported enhanced singlet exciton yield in light-emitting polymers, we investigate spin-orbit coupling between Coulombically bound interchain excitations. 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[synthetic metals, 85 (1997) 1155]" class="work-thumbnail" src="https://attachments.academia-assets.com/50667475/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/30208807/Erratum_to_density_matrix_renormalisation_group_calculations_of_molecular_exciton_energies_in_poly_phenylene_vinylene_synthetic_metals_85_1997_1155_">Erratum to ?density matrix renormalisation group calculations of molecular exciton energies in poly (-phenylene vinylene)? 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="30208805"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/30208805/Excited_states_of_linear_polyenes"><img alt="Research paper thumbnail of Excited states of linear polyenes" class="work-thumbnail" src="https://attachments.academia-assets.com/50667439/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/30208805/Excited_states_of_linear_polyenes">Excited states of linear polyenes</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We present density matrix renormalisation group calculations of the Pariser- Parr-Pople-Peierls m...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We present density matrix renormalisation group calculations of the Pariser- Parr-Pople-Peierls model of linear polyenes within the adiabatic approximation. We calculate the vertical and relaxed transition energies, and relaxed geometries for various excitations on long chains. The triplet (3Bu+) and even- parity singlet (2Ag+) states have a 2-soliton and 4-soliton form, respectively, both with large relaxation energies. The dipole-allowed (1Bu-) state forms an exciton-polaron and has a very small relaxation energy. The relaxed energy of the 2Ag+ state lies below that of the 1Bu- state. We observe an attraction between the soliton-antisoliton pairs in the 2Ag+ state. The calculated excitation energies agree well with the observed values for polyene oligomers; the agreement with polyacetylene thin films is less good, and we comment on the possible sources of the discrepencies. The photoinduced absorption is interpreted. The spin-spin correlation function shows that the unpaired spins coincide with the geometrical soliton positions. We study the roles of electron-electron interactions and electron-lattice coupling in determining the excitation energies and soliton structures. The electronic interactions play the key role in determining the ground state dimerisation and the excited state transition energies.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="270ac5630e86d4eb8c2bcb79bfbb3d30" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":50667439,"asset_id":30208805,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/50667439/download_file?st=MTczMjQ1MjAxOCw4LjIyMi4yMDguMTQ2&st=MTczMjQ1MjAxNyw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="30208805"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="30208805"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 30208805; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=30208805]").text(description); $(".js-view-count[data-work-id=30208805]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 30208805; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='30208805']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 30208805, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "270ac5630e86d4eb8c2bcb79bfbb3d30" } } $('.js-work-strip[data-work-id=30208805]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":30208805,"title":"Excited states of linear polyenes","translated_title":"","metadata":{"abstract":"We present density matrix renormalisation group calculations of the Pariser- Parr-Pople-Peierls model of linear polyenes within the adiabatic approximation. We calculate the vertical and relaxed transition energies, and relaxed geometries for various excitations on long chains. The triplet (3Bu+) and even- parity singlet (2Ag+) states have a 2-soliton and 4-soliton form, respectively, both with large relaxation energies. The dipole-allowed (1Bu-) state forms an exciton-polaron and has a very small relaxation energy. The relaxed energy of the 2Ag+ state lies below that of the 1Bu- state. We observe an attraction between the soliton-antisoliton pairs in the 2Ag+ state. The calculated excitation energies agree well with the observed values for polyene oligomers; the agreement with polyacetylene thin films is less good, and we comment on the possible sources of the discrepencies. The photoinduced absorption is interpreted. The spin-spin correlation function shows that the unpaired spins coincide with the geometrical soliton positions. We study the roles of electron-electron interactions and electron-lattice coupling in determining the excitation energies and soliton structures. The electronic interactions play the key role in determining the ground state dimerisation and the excited state transition energies.","publication_date":{"day":5,"month":3,"year":2001,"errors":{}}},"translated_abstract":"We present density matrix renormalisation group calculations of the Pariser- Parr-Pople-Peierls model of linear polyenes within the adiabatic approximation. We calculate the vertical and relaxed transition energies, and relaxed geometries for various excitations on long chains. The triplet (3Bu+) and even- parity singlet (2Ag+) states have a 2-soliton and 4-soliton form, respectively, both with large relaxation energies. The dipole-allowed (1Bu-) state forms an exciton-polaron and has a very small relaxation energy. The relaxed energy of the 2Ag+ state lies below that of the 1Bu- state. We observe an attraction between the soliton-antisoliton pairs in the 2Ag+ state. The calculated excitation energies agree well with the observed values for polyene oligomers; the agreement with polyacetylene thin films is less good, and we comment on the possible sources of the discrepencies. The photoinduced absorption is interpreted. The spin-spin correlation function shows that the unpaired spins coincide with the geometrical soliton positions. We study the roles of electron-electron interactions and electron-lattice coupling in determining the excitation energies and soliton structures. The electronic interactions play the key role in determining the ground state dimerisation and the excited state transition energies.","internal_url":"https://www.academia.edu/30208805/Excited_states_of_linear_polyenes","translated_internal_url":"","created_at":"2016-12-01T17:26:33.933-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":57527093,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[{"id":26335085,"work_id":30208805,"tagging_user_id":57527093,"tagged_user_id":null,"co_author_invite_id":5809031,"email":"m***v@bristol.ac.uk","display_order":0,"name":"Mikhail Lavrentiev","title":"Excited states of linear polyenes"},{"id":26335116,"work_id":30208805,"tagging_user_id":57527093,"tagged_user_id":null,"co_author_invite_id":5809032,"email":"w***d@sheffield.ac.uk","display_order":4194304,"name":"William Barford","title":"Excited states of linear polyenes"}],"downloadable_attachments":[{"id":50667439,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/50667439/thumbnails/1.jpg","file_name":"0103100.pdf","download_url":"https://www.academia.edu/attachments/50667439/download_file?st=MTczMjQ1MjAxOCw4LjIyMi4yMDguMTQ2&st=MTczMjQ1MjAxNyw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Excited_states_of_linear_polyenes.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/50667439/0103100-libre.pdf?1480642671=\u0026response-content-disposition=attachment%3B+filename%3DExcited_states_of_linear_polyenes.pdf\u0026Expires=1732455617\u0026Signature=XUIMvJ2sJVZHW5LTTKOzXT28xmLudOEVD91xmrartSRKnoDpATRipYvugFR-JEoa~daEq9sdadH4ikiivQqAkChTT2syOYEim0~998gm1eFoUozmncS4rx8sXTyWnQjLWBaiwvUPPBSkiAtDiOl5HGKqFk5O~9u0kVEPW2UP2hu7uSsROjmVtMa5hqbgqljmELns~iOBPn-ukpwf2ur-BTNiAmxR7uvDrd573Jbex7ZbhIgtgNWGyoehL4mFFeLWTrQ8vvewnOPt6b0MvWUO-5tKKYqUSVN0dhEJPFK7cH2G9ohLs4mbjWAt-c9ao-4G7IFkHjsX8HdVPH0w6C8dFQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Excited_states_of_linear_polyenes","translated_slug":"","page_count":23,"language":"en","content_type":"Work","owner":{"id":57527093,"first_name":"Robert","middle_initials":null,"last_name":"Bursill","page_name":"RobertBursill","domain_name":"independent","created_at":"2016-12-01T17:26:12.952-08:00","display_name":"Robert Bursill","url":"https://independent.academia.edu/RobertBursill"},"attachments":[{"id":50667439,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/50667439/thumbnails/1.jpg","file_name":"0103100.pdf","download_url":"https://www.academia.edu/attachments/50667439/download_file?st=MTczMjQ1MjAxOCw4LjIyMi4yMDguMTQ2&st=MTczMjQ1MjAxNyw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Excited_states_of_linear_polyenes.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/50667439/0103100-libre.pdf?1480642671=\u0026response-content-disposition=attachment%3B+filename%3DExcited_states_of_linear_polyenes.pdf\u0026Expires=1732455617\u0026Signature=XUIMvJ2sJVZHW5LTTKOzXT28xmLudOEVD91xmrartSRKnoDpATRipYvugFR-JEoa~daEq9sdadH4ikiivQqAkChTT2syOYEim0~998gm1eFoUozmncS4rx8sXTyWnQjLWBaiwvUPPBSkiAtDiOl5HGKqFk5O~9u0kVEPW2UP2hu7uSsROjmVtMa5hqbgqljmELns~iOBPn-ukpwf2ur-BTNiAmxR7uvDrd573Jbex7ZbhIgtgNWGyoehL4mFFeLWTrQ8vvewnOPt6b0MvWUO-5tKKYqUSVN0dhEJPFK7cH2G9ohLs4mbjWAt-c9ao-4G7IFkHjsX8HdVPH0w6C8dFQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"},{"id":50667438,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/50667438/thumbnails/1.jpg","file_name":"0103100.pdf","download_url":"https://www.academia.edu/attachments/50667438/download_file","bulk_download_file_name":"Excited_states_of_linear_polyenes.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/50667438/0103100-libre.pdf?1480642672=\u0026response-content-disposition=attachment%3B+filename%3DExcited_states_of_linear_polyenes.pdf\u0026Expires=1732455617\u0026Signature=R3pPgGr2jiJcw~TkaWmC4nR9VA5ySxKCGX52sfp3Z~92B6les9KoGM4Q3IuUFDG9pPwgfMMJs9UI8Z0ItNYK8aEQnkNQ9Lv4ly2wn9zJi1QiSLieB1dv2LuT-aoj8yf4XA6IMlk1nkx-2Nolc0FcMO3FhlOgNp~1dtVxf8~CaZoKv-0bSLrjSr88V2Mn1dj19VwuD3w4jfYNgQW0Hukr1tt6ddsSjf6wBOJe9pvT~iGJtmTAShyTuz0NV-jVH2TigPR9Hf5ywzU7NWAA~m8lq0qxtbjIcqbMJz3jRce5zEknZVtfqBMUKQPvNzUpUyH1SdRCINo8ERUVjQl3e~Ofcw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":101573,"name":"Thin Film","url":"https://www.academia.edu/Documents/in/Thin_Film"},{"id":393410,"name":"Excited states","url":"https://www.academia.edu/Documents/in/Excited_states"},{"id":435600,"name":"Density Matrix","url":"https://www.academia.edu/Documents/in/Density_Matrix"},{"id":2382100,"name":"Correlation function","url":"https://www.academia.edu/Documents/in/Correlation_function"}],"urls":[{"id":7786760,"url":"http://arxiv.org/abs/cond-mat/0103100"}]}, dispatcherData: dispatcherData }); 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The Heisenberg chain is equivalent to a spinless electron gas under a Jordan-Wigner transformation. Using density matrix renormalization group and quantum Monte Carlo methods we calculate the spin/charge stiffness of the model, which determines the strength of the 'persistent currents'. The stiffness is found to scale to zero in the weak link case, in agreement with renormalization group arguments of Eggert and Affleck, and Kane and Fisher.","publication_date":{"day":null,"month":null,"year":2002,"errors":{}},"publication_name":"Physical Review B","grobid_abstract_attachment_id":50667472},"translated_abstract":null,"internal_url":"https://www.academia.edu/30208800/Persistent_currents_in_the_Heisenberg_chain_with_a_weak_link","translated_internal_url":"","created_at":"2016-12-01T17:26:33.137-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":57527093,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[{"id":26335070,"work_id":30208800,"tagging_user_id":57527093,"tagged_user_id":null,"co_author_invite_id":5809029,"email":"c***2@student.monash.edu","display_order":0,"name":"Christopher Hamer","title":"Persistent currents in the Heisenberg chain with a weak link"},{"id":26335154,"work_id":30208800,"tagging_user_id":57527093,"tagged_user_id":null,"co_author_invite_id":2989099,"email":"s***k@buphy.bu.edu","display_order":4194304,"name":"Anders Sandvik","title":"Persistent currents in the Heisenberg chain with a weak link"},{"id":26335263,"work_id":30208800,"tagging_user_id":57527093,"tagged_user_id":42137443,"co_author_invite_id":null,"email":"t***s@colgate.edu","affiliation":"Colgate University","display_order":6291456,"name":"Timothy Byrnes","title":"Persistent currents in the Heisenberg chain with a weak link"},{"id":26335265,"work_id":30208800,"tagging_user_id":57527093,"tagged_user_id":16555052,"co_author_invite_id":null,"email":"h***e@googlemail.com","affiliation":"University of Ulm","display_order":7340032,"name":"Hans-Peter Eckle","title":"Persistent currents in the Heisenberg chain with a weak link"}],"downloadable_attachments":[{"id":50667472,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/50667472/thumbnails/1.jpg","file_name":"0deec519f79bf90952000000.pdf","download_url":"https://www.academia.edu/attachments/50667472/download_file?st=MTczMjQ1MjAxOCw4LjIyMi4yMDguMTQ2&st=MTczMjQ1MjAxOCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Persistent_currents_in_the_Heisenberg_ch.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/50667472/0deec519f79bf90952000000-libre.pdf?1480642654=\u0026response-content-disposition=attachment%3B+filename%3DPersistent_currents_in_the_Heisenberg_ch.pdf\u0026Expires=1732455618\u0026Signature=I5X1beTC5jCK~Fsf4QeB7ckMoxlPZr-1q1949Kk1LYx71bkWF8QjxUXhhkVZZGK7qENHdiO9aXjY1Z0Kw0bTwPOjeOV1xi~s2yc9GJbxxrGolLgt0GQpk9Ys4~1Wfk1CiAmsvh2vVJOo83XaTdHbddU7lzJMPgArNzxnbF2jRcLNMyQbqpKwGQYFaaZk~ZLWV15lhiyJXOWjkA5IGqJeklRGLjr~H~bRLqqFmq1DBSP-~a2xWVe2ekLQpWFy-cIfqXToze2l6AtlyycepMpuykbOOUW9Khs~LMhwbBHkgI~ID0UCCAP9G4rXeQFBuTnHKj~UNxBRiiZJ30ScWbkE0A__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Persistent_currents_in_the_Heisenberg_chain_with_a_weak_link","translated_slug":"","page_count":15,"language":"en","content_type":"Work","owner":{"id":57527093,"first_name":"Robert","middle_initials":null,"last_name":"Bursill","page_name":"RobertBursill","domain_name":"independent","created_at":"2016-12-01T17:26:12.952-08:00","display_name":"Robert Bursill","url":"https://independent.academia.edu/RobertBursill"},"attachments":[{"id":50667472,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/50667472/thumbnails/1.jpg","file_name":"0deec519f79bf90952000000.pdf","download_url":"https://www.academia.edu/attachments/50667472/download_file?st=MTczMjQ1MjAxOCw4LjIyMi4yMDguMTQ2&st=MTczMjQ1MjAxOCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Persistent_currents_in_the_Heisenberg_ch.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/50667472/0deec519f79bf90952000000-libre.pdf?1480642654=\u0026response-content-disposition=attachment%3B+filename%3DPersistent_currents_in_the_Heisenberg_ch.pdf\u0026Expires=1732455618\u0026Signature=I5X1beTC5jCK~Fsf4QeB7ckMoxlPZr-1q1949Kk1LYx71bkWF8QjxUXhhkVZZGK7qENHdiO9aXjY1Z0Kw0bTwPOjeOV1xi~s2yc9GJbxxrGolLgt0GQpk9Ys4~1Wfk1CiAmsvh2vVJOo83XaTdHbddU7lzJMPgArNzxnbF2jRcLNMyQbqpKwGQYFaaZk~ZLWV15lhiyJXOWjkA5IGqJeklRGLjr~H~bRLqqFmq1DBSP-~a2xWVe2ekLQpWFy-cIfqXToze2l6AtlyycepMpuykbOOUW9Khs~LMhwbBHkgI~ID0UCCAP9G4rXeQFBuTnHKj~UNxBRiiZJ30ScWbkE0A__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":14272,"name":"Quantum Monte Carlo","url":"https://www.academia.edu/Documents/in/Quantum_Monte_Carlo"},{"id":494966,"name":"Renormalization Group","url":"https://www.academia.edu/Documents/in/Renormalization_Group"},{"id":519863,"name":"Persistent Current","url":"https://www.academia.edu/Documents/in/Persistent_Current"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="30208799"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/30208799/Quantized_Lattice_Dynamic_Effects_on_the_Spin_Peierls_Transition"><img alt="Research paper thumbnail of Quantized Lattice Dynamic Effects on the Spin-Peierls Transition" class="work-thumbnail" src="https://attachments.academia-assets.com/50667470/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/30208799/Quantized_Lattice_Dynamic_Effects_on_the_Spin_Peierls_Transition">Quantized Lattice Dynamic Effects on the Spin-Peierls Transition</a></div><div class="wp-workCard_item"><span>Physical Review B Condensed Matter and Materials Physics</span><span>, Jul 22, 2010</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The density-matrix renormalization-group method is used to investigate the spin-Peierls transitio...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The density-matrix renormalization-group method is used to investigate the spin-Peierls transition for Heisenberg spins coupled to quantized phonons. We use a phonon spectrum that interpolates between a gapped, dispersionless (Einstein) limit to a gapless, dispersive (Debye) limit. A variety of theoretical probes are used to determine the quantum phase transition, including energy gap crossing, a finite-size scaling analysis, bond-order autocorrelation functions, and bipartite quantum entanglement. All these probes indicate that in the antiadiabatic phonon limit a quantum phase transition of the Berezinskii-Kosterlitz-Thouless type is observed at a nonzero spin-phonon coupling, gc . An extrapolation from the Einstein limit to the Debye limit is accompanied by an increase in gc for a fixed optical (q=蟺) phonon gap. We therefore conclude that the dimerized ground state is more unstable with respect to Debye phonons with the introduction of phonon-dispersion renormalizing the effective spin-lattice coupling for the Peierls-active mode. We also show that the staggered spin-spin and phonon displacement order parameters are unreliable means of determining the transition.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="51d89e31ac14041056e1ea07ca3a1c81" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":50667470,"asset_id":30208799,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/50667470/download_file?st=MTczMjQ1MjAxOCw4LjIyMi4yMDguMTQ2&st=MTczMjQ1MjAxOCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="30208799"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="30208799"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 30208799; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=30208799]").text(description); $(".js-view-count[data-work-id=30208799]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 30208799; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='30208799']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 30208799, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "51d89e31ac14041056e1ea07ca3a1c81" } } $('.js-work-strip[data-work-id=30208799]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":30208799,"title":"Quantized Lattice Dynamic Effects on the Spin-Peierls Transition","translated_title":"","metadata":{"abstract":"The density-matrix renormalization-group method is used to investigate the spin-Peierls transition for Heisenberg spins coupled to quantized phonons. We use a phonon spectrum that interpolates between a gapped, dispersionless (Einstein) limit to a gapless, dispersive (Debye) limit. A variety of theoretical probes are used to determine the quantum phase transition, including energy gap crossing, a finite-size scaling analysis, bond-order autocorrelation functions, and bipartite quantum entanglement. All these probes indicate that in the antiadiabatic phonon limit a quantum phase transition of the Berezinskii-Kosterlitz-Thouless type is observed at a nonzero spin-phonon coupling, gc . An extrapolation from the Einstein limit to the Debye limit is accompanied by an increase in gc for a fixed optical (q=蟺) phonon gap. We therefore conclude that the dimerized ground state is more unstable with respect to Debye phonons with the introduction of phonon-dispersion renormalizing the effective spin-lattice coupling for the Peierls-active mode. We also show that the staggered spin-spin and phonon displacement order parameters are unreliable means of determining the transition.","publication_date":{"day":22,"month":7,"year":2010,"errors":{}},"publication_name":"Physical Review B Condensed Matter and Materials Physics"},"translated_abstract":"The density-matrix renormalization-group method is used to investigate the spin-Peierls transition for Heisenberg spins coupled to quantized phonons. We use a phonon spectrum that interpolates between a gapped, dispersionless (Einstein) limit to a gapless, dispersive (Debye) limit. A variety of theoretical probes are used to determine the quantum phase transition, including energy gap crossing, a finite-size scaling analysis, bond-order autocorrelation functions, and bipartite quantum entanglement. All these probes indicate that in the antiadiabatic phonon limit a quantum phase transition of the Berezinskii-Kosterlitz-Thouless type is observed at a nonzero spin-phonon coupling, gc . An extrapolation from the Einstein limit to the Debye limit is accompanied by an increase in gc for a fixed optical (q=蟺) phonon gap. We therefore conclude that the dimerized ground state is more unstable with respect to Debye phonons with the introduction of phonon-dispersion renormalizing the effective spin-lattice coupling for the Peierls-active mode. We also show that the staggered spin-spin and phonon displacement order parameters are unreliable means of determining the transition.","internal_url":"https://www.academia.edu/30208799/Quantized_Lattice_Dynamic_Effects_on_the_Spin_Peierls_Transition","translated_internal_url":"","created_at":"2016-12-01T17:26:32.954-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":57527093,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[{"id":26335114,"work_id":30208799,"tagging_user_id":57527093,"tagged_user_id":null,"co_author_invite_id":5809032,"email":"w***d@sheffield.ac.uk","display_order":0,"name":"William Barford","title":"Quantized Lattice Dynamic Effects on the Spin-Peierls Transition"},{"id":26335132,"work_id":30208799,"tagging_user_id":57527093,"tagged_user_id":null,"co_author_invite_id":5809038,"email":"c***n@internode.on.net","display_order":4194304,"name":"Christopher Pearson","title":"Quantized Lattice Dynamic Effects on the Spin-Peierls Transition"}],"downloadable_attachments":[{"id":50667470,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/50667470/thumbnails/1.jpg","file_name":"1007.3860.pdf","download_url":"https://www.academia.edu/attachments/50667470/download_file?st=MTczMjQ1MjAxOCw4LjIyMi4yMDguMTQ2&st=MTczMjQ1MjAxOCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Quantized_Lattice_Dynamic_Effects_on_the.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/50667470/1007.3860-libre.pdf?1480642658=\u0026response-content-disposition=attachment%3B+filename%3DQuantized_Lattice_Dynamic_Effects_on_the.pdf\u0026Expires=1732455618\u0026Signature=gCNFhEz1rEcAydafQvL6mx43oeC8u8OTC6ElfBqTaJaBsu3-Kb5otH~nZWtsHgFMhKP2yc~t6ZJVxrbaFiUlCXndN75NN78gqzceDC3JhwZ9xDYPemPJcHWuinldh3-ecKifUrRAvUWwW-HqvDGTXtG194z1fjIHC6eLXYzgpd3briSmGLO--e3FTO2XKyAZNabUHPogeSTIH~Q01ylZVF94MRgowJ9FXsSVVaw9nigr5iXKIODrPIfmtCo6CLpQ79tal3x005nL8kgFvW3OqaF00bP20OGggKtZlKfiHGuV4NroFa2H7yOT8waq6AswSJIIgZqG4KNKIWXaiJrBfg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Quantized_Lattice_Dynamic_Effects_on_the_Spin_Peierls_Transition","translated_slug":"","page_count":24,"language":"en","content_type":"Work","owner":{"id":57527093,"first_name":"Robert","middle_initials":null,"last_name":"Bursill","page_name":"RobertBursill","domain_name":"independent","created_at":"2016-12-01T17:26:12.952-08:00","display_name":"Robert Bursill","url":"https://independent.academia.edu/RobertBursill"},"attachments":[{"id":50667470,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/50667470/thumbnails/1.jpg","file_name":"1007.3860.pdf","download_url":"https://www.academia.edu/attachments/50667470/download_file?st=MTczMjQ1MjAxOCw4LjIyMi4yMDguMTQ2&st=MTczMjQ1MjAxOCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Quantized_Lattice_Dynamic_Effects_on_the.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/50667470/1007.3860-libre.pdf?1480642658=\u0026response-content-disposition=attachment%3B+filename%3DQuantized_Lattice_Dynamic_Effects_on_the.pdf\u0026Expires=1732455618\u0026Signature=gCNFhEz1rEcAydafQvL6mx43oeC8u8OTC6ElfBqTaJaBsu3-Kb5otH~nZWtsHgFMhKP2yc~t6ZJVxrbaFiUlCXndN75NN78gqzceDC3JhwZ9xDYPemPJcHWuinldh3-ecKifUrRAvUWwW-HqvDGTXtG194z1fjIHC6eLXYzgpd3briSmGLO--e3FTO2XKyAZNabUHPogeSTIH~Q01ylZVF94MRgowJ9FXsSVVaw9nigr5iXKIODrPIfmtCo6CLpQ79tal3x005nL8kgFvW3OqaF00bP20OGggKtZlKfiHGuV4NroFa2H7yOT8waq6AswSJIIgZqG4KNKIWXaiJrBfg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":43591,"name":"Quantum entanglement","url":"https://www.academia.edu/Documents/in/Quantum_entanglement"},{"id":118582,"name":"Physical sciences","url":"https://www.academia.edu/Documents/in/Physical_sciences"},{"id":260118,"name":"CHEMICAL SCIENCES","url":"https://www.academia.edu/Documents/in/CHEMICAL_SCIENCES"},{"id":321836,"name":"Spectrum","url":"https://www.academia.edu/Documents/in/Spectrum"},{"id":983074,"name":"Quantum Phase Transition","url":"https://www.academia.edu/Documents/in/Quantum_Phase_Transition"},{"id":1118571,"name":"Autocorrelation Function","url":"https://www.academia.edu/Documents/in/Autocorrelation_Function"}],"urls":[{"id":7786756,"url":"http://adsabs.harvard.edu/abs/2010PhRvB..82n4408P"}]}, dispatcherData: dispatcherData }); 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