Adiabatic Eigenstate Deformations as a Sensitive Probe for Quantum Chaos

In the past decades, it was recognized that quantum chaos, which is essential for the emergence of statistical mechanics and thermodynamics, manifests itself in the effective description of the eigenstates of chaotic Hamiltonians through random matrix ensembles and the eigenstate thermalization hypo...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Mohit Pandey, Pieter W. Claeys, David K. Campbell, Anatoli Polkovnikov, Dries Sels
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2020
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/9ffdb471ddb9435c938eb8e358f9a7f2
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:9ffdb471ddb9435c938eb8e358f9a7f2
record_format	dspace
spelling	oai:doaj.org-article:9ffdb471ddb9435c938eb8e358f9a7f22021-12-02T12:21:29ZAdiabatic Eigenstate Deformations as a Sensitive Probe for Quantum Chaos10.1103/PhysRevX.10.0410172160-3308https://doaj.org/article/9ffdb471ddb9435c938eb8e358f9a7f22020-10-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.10.041017http://doi.org/10.1103/PhysRevX.10.041017https://doaj.org/toc/2160-3308In the past decades, it was recognized that quantum chaos, which is essential for the emergence of statistical mechanics and thermodynamics, manifests itself in the effective description of the eigenstates of chaotic Hamiltonians through random matrix ensembles and the eigenstate thermalization hypothesis. Standard measures of chaos in quantum many-body systems are level statistics and the spectral form factor. In this work, we show that the norm of the adiabatic gauge potential, the generator of adiabatic deformations between eigenstates, serves as a much more sensitive measure of quantum chaos. We are able to detect transitions from integrable to chaotic behavior at perturbation strengths orders of magnitude smaller than those required for standard measures. Using this alternative probe in two generic classes of spin chains, we show that the chaotic threshold decreases exponentially with system size and that one can immediately detect integrability-breaking (chaotic) perturbations by analyzing infinitesimal perturbations even at the integrable point. In some cases, small integrability breaking is shown to lead to anomalously slow relaxation of the system, exponentially long in system size.Mohit PandeyPieter W. ClaeysDavid K. CampbellAnatoli PolkovnikovDries SelsAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 10, Iss 4, p 041017 (2020)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Mohit Pandey Pieter W. Claeys David K. Campbell Anatoli Polkovnikov Dries Sels Adiabatic Eigenstate Deformations as a Sensitive Probe for Quantum Chaos
description	In the past decades, it was recognized that quantum chaos, which is essential for the emergence of statistical mechanics and thermodynamics, manifests itself in the effective description of the eigenstates of chaotic Hamiltonians through random matrix ensembles and the eigenstate thermalization hypothesis. Standard measures of chaos in quantum many-body systems are level statistics and the spectral form factor. In this work, we show that the norm of the adiabatic gauge potential, the generator of adiabatic deformations between eigenstates, serves as a much more sensitive measure of quantum chaos. We are able to detect transitions from integrable to chaotic behavior at perturbation strengths orders of magnitude smaller than those required for standard measures. Using this alternative probe in two generic classes of spin chains, we show that the chaotic threshold decreases exponentially with system size and that one can immediately detect integrability-breaking (chaotic) perturbations by analyzing infinitesimal perturbations even at the integrable point. In some cases, small integrability breaking is shown to lead to anomalously slow relaxation of the system, exponentially long in system size.
format	article
author	Mohit Pandey Pieter W. Claeys David K. Campbell Anatoli Polkovnikov Dries Sels
author_facet	Mohit Pandey Pieter W. Claeys David K. Campbell Anatoli Polkovnikov Dries Sels
author_sort	Mohit Pandey
title	Adiabatic Eigenstate Deformations as a Sensitive Probe for Quantum Chaos
title_short	Adiabatic Eigenstate Deformations as a Sensitive Probe for Quantum Chaos
title_full	Adiabatic Eigenstate Deformations as a Sensitive Probe for Quantum Chaos
title_fullStr	Adiabatic Eigenstate Deformations as a Sensitive Probe for Quantum Chaos
title_full_unstemmed	Adiabatic Eigenstate Deformations as a Sensitive Probe for Quantum Chaos
title_sort	adiabatic eigenstate deformations as a sensitive probe for quantum chaos
publisher	American Physical Society
publishDate	2020
url	https://doaj.org/article/9ffdb471ddb9435c938eb8e358f9a7f2
work_keys_str_mv	AT mohitpandey adiabaticeigenstatedeformationsasasensitiveprobeforquantumchaos AT pieterwclaeys adiabaticeigenstatedeformationsasasensitiveprobeforquantumchaos AT davidkcampbell adiabaticeigenstatedeformationsasasensitiveprobeforquantumchaos AT anatolipolkovnikov adiabaticeigenstatedeformationsasasensitiveprobeforquantumchaos AT driessels adiabaticeigenstatedeformationsasasensitiveprobeforquantumchaos
_version_	1718394529184219136

Adiabatic Eigenstate Deformations as a Sensitive Probe for Quantum Chaos

Ejemplares similares