Abstract
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.
- Received 10 April 2020
- Accepted 14 September 2020
DOI:https://doi.org/10.1103/PhysRevX.10.041017
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Quantum chaos and ergodicity, which underlies all of statistical mechanics and thermodynamics, manifests itself in a vast range of phenomena. While researchers have developed powerful mathematical tools for understanding the emergence of chaos in quantum systems, the same cannot be said for probes that verify that the system is indeed chaotic. Although standard measures of quantum chaos exist, they are generally not very sensitive. We propose a sensitive probe for quantum chaos that is in line with both quantum and classical definitions of chaos.
To understand the emergence of chaos in quantum systems, researchers rely on the eigenstate thermalization hypothesis. Briefly, the hypothesis says that quantum chaos is encoded in the set of allowed energy states of a quantum system, as opposed to classical chaos which is expressed through exponential sensitivity of particle trajectories to initial conditions. Our proposed probe of quantum chaos blends both definitions by quantifying the sensitivity of allowed energy states to small perturbations. Using an appropriate measure, we can detect quantum chaos orders of magnitude before standard measures and extract information about nontrivial dynamics close to nonchaotic regimes. We use this probe to establish the existence of a regime separating nonchaotic and chaotic systems, characterized by a maximal sensitivity of allowed energy states and anomalously slow (exponentially long) relaxation times.
This work shows that there is a maximally susceptible regime separating chaotic and nonchaotic systems. Our measure can probe this regime, which is completely invisible to standard measures such as level-spacing statistics.
