Uhlmann number in translational invariant systems

We define the Uhlmann number as an extension of the Chern number, and we use this quantity to describe the topology of 2D translational invariant Fermionic systems at finite temperature. We consider two paradigmatic systems and we study the changes in their topology through the Uhlmann number. Throu...

Descripción completa

Detalles Bibliográficos
Autores principales: Leonforte, Luca, Valenti, Davide, Spagnolo, Bernardo, Carollo, Angelo
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group UK 2019
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6591291/
https://www.ncbi.nlm.nih.gov/pubmed/31235825
http://dx.doi.org/10.1038/s41598-019-45546-9
_version_ 1783429700247355392
author Leonforte, Luca
Valenti, Davide
Spagnolo, Bernardo
Carollo, Angelo
author_facet Leonforte, Luca
Valenti, Davide
Spagnolo, Bernardo
Carollo, Angelo
author_sort Leonforte, Luca
collection PubMed
description We define the Uhlmann number as an extension of the Chern number, and we use this quantity to describe the topology of 2D translational invariant Fermionic systems at finite temperature. We consider two paradigmatic systems and we study the changes in their topology through the Uhlmann number. Through the linear response theory we link two geometrical quantities of the system, the mean Uhlmann curvature and the Uhlmann number, to directly measurable physical quantities, i.e. the dynamical susceptibility and the dynamical conductivity, respectively. In particular, we derive a non-zero temperature generalisation of the Thouless-Kohmoto-Nightingale-den Nijs formula.
format Online
Article
Text
id pubmed-6591291
institution National Center for Biotechnology Information
language English
publishDate 2019
publisher Nature Publishing Group UK
record_format MEDLINE/PubMed
spelling pubmed-65912912019-07-02 Uhlmann number in translational invariant systems Leonforte, Luca Valenti, Davide Spagnolo, Bernardo Carollo, Angelo Sci Rep Article We define the Uhlmann number as an extension of the Chern number, and we use this quantity to describe the topology of 2D translational invariant Fermionic systems at finite temperature. We consider two paradigmatic systems and we study the changes in their topology through the Uhlmann number. Through the linear response theory we link two geometrical quantities of the system, the mean Uhlmann curvature and the Uhlmann number, to directly measurable physical quantities, i.e. the dynamical susceptibility and the dynamical conductivity, respectively. In particular, we derive a non-zero temperature generalisation of the Thouless-Kohmoto-Nightingale-den Nijs formula. Nature Publishing Group UK 2019-06-24 /pmc/articles/PMC6591291/ /pubmed/31235825 http://dx.doi.org/10.1038/s41598-019-45546-9 Text en © The Author(s) 2019 Open Access This 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 license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license 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 license, visit http://creativecommons.org/licenses/by/4.0/.
spellingShingle Article
Leonforte, Luca
Valenti, Davide
Spagnolo, Bernardo
Carollo, Angelo
Uhlmann number in translational invariant systems
title Uhlmann number in translational invariant systems
title_full Uhlmann number in translational invariant systems
title_fullStr Uhlmann number in translational invariant systems
title_full_unstemmed Uhlmann number in translational invariant systems
title_short Uhlmann number in translational invariant systems
title_sort uhlmann number in translational invariant systems
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6591291/
https://www.ncbi.nlm.nih.gov/pubmed/31235825
http://dx.doi.org/10.1038/s41598-019-45546-9
work_keys_str_mv AT leonforteluca uhlmannnumberintranslationalinvariantsystems
AT valentidavide uhlmannnumberintranslationalinvariantsystems
AT spagnolobernardo uhlmannnumberintranslationalinvariantsystems
AT carolloangelo uhlmannnumberintranslationalinvariantsystems

Ejemplares similares