Density-matrix Chern insulators: finite-temperature generalization of topological insulators

Thermal noise can destroy topological insulators (TI). However, we demonstrate how TIs can be made stable in dissipative systems. To that aim, we introduce the notion of band Liouvillian as the dissipative counterpart of band Hamiltonian, and show a method to evaluate the topological order of its st...

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Detalles Bibliográficos
Autores: Rivas Vargas, Ángel, Viyuela García, Óscar, Martín-Delgado Alcántara, Miguel Ángel
Tipo de recurso: artículo
Fecha de publicación:2013
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/35608
Acceso en línea:https://hdl.handle.net/20.500.14352/35608
Access Level:acceso abierto
Palabra clave:53
Markovian master equations
Quantized hall conductance
State
Phase
Dissipation.
Física-Modelos matemáticos
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spelling Density-matrix Chern insulators: finite-temperature generalization of topological insulatorsRivas Vargas, ÁngelViyuela García, ÓscarMartín-Delgado Alcántara, Miguel Ángel53Markovian master equationsQuantized hall conductanceStatePhaseDissipation.Física-Modelos matemáticosThermal noise can destroy topological insulators (TI). However, we demonstrate how TIs can be made stable in dissipative systems. To that aim, we introduce the notion of band Liouvillian as the dissipative counterpart of band Hamiltonian, and show a method to evaluate the topological order of its steady state. This is based on a generalization of the Chern number valid for general mixed states (referred to as density-matrix Chern value), which witnesses topological order in a system coupled to external noise. Additionally, we study its relation with the electrical conductivity at finite temperature, which is not a topological property. Nonetheless, the density-matrix Chern value represents the part of the conductivity which is topological due to the presence of quantum mixed edge states at finite temperature. To make our formalism concrete, we apply these concepts to the two-dimensional Haldane model in the presence of thermal dissipation, but our results hold for arbitrary dimensions and density matrices.American Physical SocietyUniversidad Complutense de Madrid20132013-10-3120132013-10-31journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/35608reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/356082026-06-02T12:44:21Z
dc.title.none.fl_str_mv Density-matrix Chern insulators: finite-temperature generalization of topological insulators
title Density-matrix Chern insulators: finite-temperature generalization of topological insulators
spellingShingle Density-matrix Chern insulators: finite-temperature generalization of topological insulators
Rivas Vargas, Ángel
53
Markovian master equations
Quantized hall conductance
State
Phase
Dissipation.
Física-Modelos matemáticos
title_short Density-matrix Chern insulators: finite-temperature generalization of topological insulators
title_full Density-matrix Chern insulators: finite-temperature generalization of topological insulators
title_fullStr Density-matrix Chern insulators: finite-temperature generalization of topological insulators
title_full_unstemmed Density-matrix Chern insulators: finite-temperature generalization of topological insulators
title_sort Density-matrix Chern insulators: finite-temperature generalization of topological insulators
dc.creator.none.fl_str_mv Rivas Vargas, Ángel
Viyuela García, Óscar
Martín-Delgado Alcántara, Miguel Ángel
author Rivas Vargas, Ángel
author_facet Rivas Vargas, Ángel
Viyuela García, Óscar
Martín-Delgado Alcántara, Miguel Ángel
author_role author
author2 Viyuela García, Óscar
Martín-Delgado Alcántara, Miguel Ángel
author2_role author
author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 53
Markovian master equations
Quantized hall conductance
State
Phase
Dissipation.
Física-Modelos matemáticos
topic 53
Markovian master equations
Quantized hall conductance
State
Phase
Dissipation.
Física-Modelos matemáticos
description Thermal noise can destroy topological insulators (TI). However, we demonstrate how TIs can be made stable in dissipative systems. To that aim, we introduce the notion of band Liouvillian as the dissipative counterpart of band Hamiltonian, and show a method to evaluate the topological order of its steady state. This is based on a generalization of the Chern number valid for general mixed states (referred to as density-matrix Chern value), which witnesses topological order in a system coupled to external noise. Additionally, we study its relation with the electrical conductivity at finite temperature, which is not a topological property. Nonetheless, the density-matrix Chern value represents the part of the conductivity which is topological due to the presence of quantum mixed edge states at finite temperature. To make our formalism concrete, we apply these concepts to the two-dimensional Haldane model in the presence of thermal dissipation, but our results hold for arbitrary dimensions and density matrices.
publishDate 2013
dc.date.none.fl_str_mv 2013
2013-10-31
2013
2013-10-31
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/35608
url https://hdl.handle.net/20.500.14352/35608
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv American Physical Society
publisher.none.fl_str_mv American Physical Society
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300719

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