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Quench in the 1D Bose-Hubbard model: Topological defects and excitations from the Kosterlitz-Thouless phase transition dynamics

Kibble-Zurek mechanism (KZM) uses critical scaling to predict density of topological defects and other excitations created in second order phase transitions. We point out that simply inserting asymptotic critical exponents deduced from the immediate vicinity of the critical point to obtain predictio...

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Detalles Bibliográficos
Autores principales: Dziarmaga, Jacek, Zurek, Wojciech H.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group 2014
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4121610/
https://www.ncbi.nlm.nih.gov/pubmed/25091996
http://dx.doi.org/10.1038/srep05950
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author Dziarmaga, Jacek
Zurek, Wojciech H.
author_facet Dziarmaga, Jacek
Zurek, Wojciech H.
author_sort Dziarmaga, Jacek
collection PubMed
description Kibble-Zurek mechanism (KZM) uses critical scaling to predict density of topological defects and other excitations created in second order phase transitions. We point out that simply inserting asymptotic critical exponents deduced from the immediate vicinity of the critical point to obtain predictions can lead to results that are inconsistent with a more careful KZM analysis based on causality – on the comparison of the relaxation time of the order parameter with the “time distance” from the critical point. As a result, scaling of quench-generated excitations with quench rates can exhibit behavior that is locally (i.e., in the neighborhood of any given quench rate) well approximated by the power law, but with exponents that depend on that rate, and that are quite different from the naive prediction based on the critical exponents relevant for asymptotically long quench times. Kosterlitz-Thouless scaling (that governs e.g. Mott insulator to superfluid transition in the Bose-Hubbard model in one dimension) is investigated as an example of this phenomenon.
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spelling pubmed-41216102014-08-14 Quench in the 1D Bose-Hubbard model: Topological defects and excitations from the Kosterlitz-Thouless phase transition dynamics Dziarmaga, Jacek Zurek, Wojciech H. Sci Rep Article Kibble-Zurek mechanism (KZM) uses critical scaling to predict density of topological defects and other excitations created in second order phase transitions. We point out that simply inserting asymptotic critical exponents deduced from the immediate vicinity of the critical point to obtain predictions can lead to results that are inconsistent with a more careful KZM analysis based on causality – on the comparison of the relaxation time of the order parameter with the “time distance” from the critical point. As a result, scaling of quench-generated excitations with quench rates can exhibit behavior that is locally (i.e., in the neighborhood of any given quench rate) well approximated by the power law, but with exponents that depend on that rate, and that are quite different from the naive prediction based on the critical exponents relevant for asymptotically long quench times. Kosterlitz-Thouless scaling (that governs e.g. Mott insulator to superfluid transition in the Bose-Hubbard model in one dimension) is investigated as an example of this phenomenon. Nature Publishing Group 2014-08-05 /pmc/articles/PMC4121610/ /pubmed/25091996 http://dx.doi.org/10.1038/srep05950 Text en Copyright © 2014, Macmillan Publishers Limited. All rights reserved http://creativecommons.org/licenses/by/4.0/ This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder in order to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/
spellingShingle Article
Dziarmaga, Jacek
Zurek, Wojciech H.
Quench in the 1D Bose-Hubbard model: Topological defects and excitations from the Kosterlitz-Thouless phase transition dynamics
title Quench in the 1D Bose-Hubbard model: Topological defects and excitations from the Kosterlitz-Thouless phase transition dynamics
title_full Quench in the 1D Bose-Hubbard model: Topological defects and excitations from the Kosterlitz-Thouless phase transition dynamics
title_fullStr Quench in the 1D Bose-Hubbard model: Topological defects and excitations from the Kosterlitz-Thouless phase transition dynamics
title_full_unstemmed Quench in the 1D Bose-Hubbard model: Topological defects and excitations from the Kosterlitz-Thouless phase transition dynamics
title_short Quench in the 1D Bose-Hubbard model: Topological defects and excitations from the Kosterlitz-Thouless phase transition dynamics
title_sort quench in the 1d bose-hubbard model: topological defects and excitations from the kosterlitz-thouless phase transition dynamics
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4121610/
https://www.ncbi.nlm.nih.gov/pubmed/25091996
http://dx.doi.org/10.1038/srep05950
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