Free energy asymptotics of the quantum Heisenberg spin chain

We consider the ferromagnetic quantum Heisenberg model in one dimension, for any spin [Formula: see text] . We give upper and lower bounds on the free energy, proving that at low temperature it is asymptotically equal to the one of an ideal Bose gas of magnons, as predicted by the spin-wave approxim...

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Autores principales: Napiórkowski, Marcin, Seiringer, Robert
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Netherlands 2021
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7943535/
https://www.ncbi.nlm.nih.gov/pubmed/33785980
http://dx.doi.org/10.1007/s11005-021-01375-4
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author Napiórkowski, Marcin
Seiringer, Robert
author_facet Napiórkowski, Marcin
Seiringer, Robert
author_sort Napiórkowski, Marcin
collection PubMed
description We consider the ferromagnetic quantum Heisenberg model in one dimension, for any spin [Formula: see text] . We give upper and lower bounds on the free energy, proving that at low temperature it is asymptotically equal to the one of an ideal Bose gas of magnons, as predicted by the spin-wave approximation. The trial state used in the upper bound yields an analogous estimate also in the case of two spatial dimensions, which is believed to be sharp at low temperature.
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spelling pubmed-79435352021-03-28 Free energy asymptotics of the quantum Heisenberg spin chain Napiórkowski, Marcin Seiringer, Robert Lett Math Phys Article We consider the ferromagnetic quantum Heisenberg model in one dimension, for any spin [Formula: see text] . We give upper and lower bounds on the free energy, proving that at low temperature it is asymptotically equal to the one of an ideal Bose gas of magnons, as predicted by the spin-wave approximation. The trial state used in the upper bound yields an analogous estimate also in the case of two spatial dimensions, which is believed to be sharp at low temperature. Springer Netherlands 2021-03-09 2021 /pmc/articles/PMC7943535/ /pubmed/33785980 http://dx.doi.org/10.1007/s11005-021-01375-4 Text en © The Author(s) 2021 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Napiórkowski, Marcin
Seiringer, Robert
Free energy asymptotics of the quantum Heisenberg spin chain
title Free energy asymptotics of the quantum Heisenberg spin chain
title_full Free energy asymptotics of the quantum Heisenberg spin chain
title_fullStr Free energy asymptotics of the quantum Heisenberg spin chain
title_full_unstemmed Free energy asymptotics of the quantum Heisenberg spin chain
title_short Free energy asymptotics of the quantum Heisenberg spin chain
title_sort free energy asymptotics of the quantum heisenberg spin chain
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7943535/
https://www.ncbi.nlm.nih.gov/pubmed/33785980
http://dx.doi.org/10.1007/s11005-021-01375-4
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