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...
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American Physical Society
2020-10-01
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Series: | Physical Review X |
Online Access: | http://doi.org/10.1103/PhysRevX.10.041017 |
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doaj-9ffdb471ddb9435c938eb8e358f9a7f22020-11-25T03:43:51ZengAmerican Physical SocietyPhysical Review X2160-33082020-10-0110404101710.1103/PhysRevX.10.041017Adiabatic Eigenstate Deformations as a Sensitive Probe for Quantum ChaosMohit PandeyPieter W. ClaeysDavid K. CampbellAnatoli PolkovnikovDries SelsIn 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.http://doi.org/10.1103/PhysRevX.10.041017 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Mohit Pandey Pieter W. Claeys David K. Campbell Anatoli Polkovnikov Dries Sels |
spellingShingle |
Mohit Pandey Pieter W. Claeys David K. Campbell Anatoli Polkovnikov Dries Sels Adiabatic Eigenstate Deformations as a Sensitive Probe for Quantum Chaos Physical Review X |
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 |
series |
Physical Review X |
issn |
2160-3308 |
publishDate |
2020-10-01 |
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. |
url |
http://doi.org/10.1103/PhysRevX.10.041017 |
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