Symmetry violation of quantum multifractality: Gaussian fluctuations versus algebraic localization

Autores
Bilen, Agustín Miguel; Georgeot, B.; Giraud, O.; Lemarié, G.; Garcia-Mata, Ignacio
Año de publicación
2021
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Quantum multifractality is a fundamental property of systems such as noninteracting disordered systems at an Anderson transition and many-body systems in Hilbert space. Here we discuss the origin of the presence or absence of a fundamental symmetry related to this property. The anomalous multifractal dimension Δq is used to characterize the structure of quantum states in such systems. Although the multifractal symmetry relation Δq=Δ1-q is universally fulfilled in many known systems, recently some important examples have emerged where it does not hold. We show that this is the result of two different mechanisms. The first one was already known and is related to Gaussian fluctuations well described by random matrix theory. The second one, not previously explored, is related to the presence of an algebraically localized envelope. While the effect of Gaussian fluctuations can be removed by coarse graining, the second mechanism is robust to such a procedure. We illustrate the violation of the symmetry due to algebraic localization on two systems of very different nature, a 1D Floquet critical system and a model corresponding to Anderson localization on random graphs.
Fil: Bilen, Agustín Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; Argentina
Fil: Georgeot, B.. Universite de Toulouse; Francia
Fil: Giraud, O.. Université Paris Saclay; Francia
Fil: Lemarié, G.. Universite de Toulouse; Francia
Fil: Garcia-Mata, Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; Argentina
Materia
QUANTUM
MULTIFRACTALITY
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/173816
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Symmetry violation of quantum multifractality: Gaussian fluctuations versus algebraic localizationBilen, Agustín MiguelGeorgeot, B.Giraud, O.Lemarié, G.Garcia-Mata, IgnacioQUANTUMMULTIFRACTALITYhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1Quantum multifractality is a fundamental property of systems such as noninteracting disordered systems at an Anderson transition and many-body systems in Hilbert space. Here we discuss the origin of the presence or absence of a fundamental symmetry related to this property. The anomalous multifractal dimension Δq is used to characterize the structure of quantum states in such systems. Although the multifractal symmetry relation Δq=Δ1-q is universally fulfilled in many known systems, recently some important examples have emerged where it does not hold. We show that this is the result of two different mechanisms. The first one was already known and is related to Gaussian fluctuations well described by random matrix theory. The second one, not previously explored, is related to the presence of an algebraically localized envelope. While the effect of Gaussian fluctuations can be removed by coarse graining, the second mechanism is robust to such a procedure. We illustrate the violation of the symmetry due to algebraic localization on two systems of very different nature, a 1D Floquet critical system and a model corresponding to Anderson localization on random graphs.Fil: Bilen, Agustín Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; ArgentinaFil: Georgeot, B.. Universite de Toulouse; FranciaFil: Giraud, O.. Université Paris Saclay; FranciaFil: Lemarié, G.. Universite de Toulouse; FranciaFil: Garcia-Mata, Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; ArgentinaAmerican Physical Society2021-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/173816Bilen, Agustín Miguel; Georgeot, B.; Giraud, O.; Lemarié, G.; Garcia-Mata, Ignacio; Symmetry violation of quantum multifractality: Gaussian fluctuations versus algebraic localization; American Physical Society; Physical Review Research; 3; 2; 6-2021; 1-82643-1564CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.aps.org/doi/10.1103/PhysRevResearch.3.L022023info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevResearch.3.L022023info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:36:34Zoai:ri.conicet.gov.ar:11336/173816instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 09:36:34.362CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Symmetry violation of quantum multifractality: Gaussian fluctuations versus algebraic localization
title Symmetry violation of quantum multifractality: Gaussian fluctuations versus algebraic localization
spellingShingle Symmetry violation of quantum multifractality: Gaussian fluctuations versus algebraic localization
Bilen, Agustín Miguel
QUANTUM
MULTIFRACTALITY
title_short Symmetry violation of quantum multifractality: Gaussian fluctuations versus algebraic localization
title_full Symmetry violation of quantum multifractality: Gaussian fluctuations versus algebraic localization
title_fullStr Symmetry violation of quantum multifractality: Gaussian fluctuations versus algebraic localization
title_full_unstemmed Symmetry violation of quantum multifractality: Gaussian fluctuations versus algebraic localization
title_sort Symmetry violation of quantum multifractality: Gaussian fluctuations versus algebraic localization
dc.creator.none.fl_str_mv Bilen, Agustín Miguel
Georgeot, B.
Giraud, O.
Lemarié, G.
Garcia-Mata, Ignacio
author Bilen, Agustín Miguel
author_facet Bilen, Agustín Miguel
Georgeot, B.
Giraud, O.
Lemarié, G.
Garcia-Mata, Ignacio
author_role author
author2 Georgeot, B.
Giraud, O.
Lemarié, G.
Garcia-Mata, Ignacio
author2_role author
author
author
author
dc.subject.none.fl_str_mv QUANTUM
MULTIFRACTALITY
topic QUANTUM
MULTIFRACTALITY
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Quantum multifractality is a fundamental property of systems such as noninteracting disordered systems at an Anderson transition and many-body systems in Hilbert space. Here we discuss the origin of the presence or absence of a fundamental symmetry related to this property. The anomalous multifractal dimension Δq is used to characterize the structure of quantum states in such systems. Although the multifractal symmetry relation Δq=Δ1-q is universally fulfilled in many known systems, recently some important examples have emerged where it does not hold. We show that this is the result of two different mechanisms. The first one was already known and is related to Gaussian fluctuations well described by random matrix theory. The second one, not previously explored, is related to the presence of an algebraically localized envelope. While the effect of Gaussian fluctuations can be removed by coarse graining, the second mechanism is robust to such a procedure. We illustrate the violation of the symmetry due to algebraic localization on two systems of very different nature, a 1D Floquet critical system and a model corresponding to Anderson localization on random graphs.
Fil: Bilen, Agustín Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; Argentina
Fil: Georgeot, B.. Universite de Toulouse; Francia
Fil: Giraud, O.. Université Paris Saclay; Francia
Fil: Lemarié, G.. Universite de Toulouse; Francia
Fil: Garcia-Mata, Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; Argentina
description Quantum multifractality is a fundamental property of systems such as noninteracting disordered systems at an Anderson transition and many-body systems in Hilbert space. Here we discuss the origin of the presence or absence of a fundamental symmetry related to this property. The anomalous multifractal dimension Δq is used to characterize the structure of quantum states in such systems. Although the multifractal symmetry relation Δq=Δ1-q is universally fulfilled in many known systems, recently some important examples have emerged where it does not hold. We show that this is the result of two different mechanisms. The first one was already known and is related to Gaussian fluctuations well described by random matrix theory. The second one, not previously explored, is related to the presence of an algebraically localized envelope. While the effect of Gaussian fluctuations can be removed by coarse graining, the second mechanism is robust to such a procedure. We illustrate the violation of the symmetry due to algebraic localization on two systems of very different nature, a 1D Floquet critical system and a model corresponding to Anderson localization on random graphs.
publishDate 2021
dc.date.none.fl_str_mv 2021-06
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/173816
Bilen, Agustín Miguel; Georgeot, B.; Giraud, O.; Lemarié, G.; Garcia-Mata, Ignacio; Symmetry violation of quantum multifractality: Gaussian fluctuations versus algebraic localization; American Physical Society; Physical Review Research; 3; 2; 6-2021; 1-8
2643-1564
CONICET Digital
CONICET
url http://hdl.handle.net/11336/173816
identifier_str_mv Bilen, Agustín Miguel; Georgeot, B.; Giraud, O.; Lemarié, G.; Garcia-Mata, Ignacio; Symmetry violation of quantum multifractality: Gaussian fluctuations versus algebraic localization; American Physical Society; Physical Review Research; 3; 2; 6-2021; 1-8
2643-1564
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://link.aps.org/doi/10.1103/PhysRevResearch.3.L022023
info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevResearch.3.L022023
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
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:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.070432

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