Quantum Lyapunov spectrum

Gharibyan, Hrant; Hanada, Masanori; Swingle, Brian; Tezuka, Masaki

doi:10.1007/jhep04(2019)082

Quantum Lyapunov spectrum

Journal Article · Wed Apr 10 00:00:00 EDT 2019 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep04(2019)082· OSTI ID:1612780

Gharibyan, Hrant ^[1]; ^[2]; Swingle, Brian ^[3]; ^[4]

Stanford Univ., CA (United States). Stanford Inst. of Theoretical Physics (ITP); DOE/OSTI
Univ. of Colorado, Boulder, CO (United States). Dept. of Physics
Univ. of Maryland, College Park, MD (United States). Dept. of Physics
Kyoto Univ. (Japan)

We introduce a simple quantum generalization of the spectrum of classical Lyapunov exponents. We apply it to the SYK and XXZ models, and study the Lyapunov growth and entropy production. Our numerical results suggest that a black hole is not just the fastest scrambler, but also the fastest entropy generator. We also study the statistical features of the quantum Lyapunov spectrum and find universal random matrix behavior, which resembles the recently-found universality in classical chaos. The random matrix behavior is lost when the system is deformed away from chaos, towards integrability or a many-body localized phase. We propose that quantum systems holographically dual to gravity satisfy this universality in a strong form. We further argue that the quantum Lyapunov spectrum contains important additional information beyond the largest Lyapunov exponent and hence provides us with a better characterization of chaos in quantum systems.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Colorado, Boulder, CO (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0017905

OSTI ID:: 1612780

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 4 Vol. 2019; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Detecting equilibrium and dynamical quantum phase transitions in Ising chains via out-of-time-ordered correlators Heyl, Markus; Pollmann, Frank; Dóra, Balázs arXiv https://doi.org/10.48550/arxiv.1801.01684	text	January 2018
Entanglement Features of Random Hamiltonian Dynamics You, Yi-Zhuang; Gu, Yingfei arXiv https://doi.org/10.48550/arxiv.1803.10425	text	January 2018
Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states Basko, D. M.; Aleiner, I. L.; Altshuler, B. L. arXiv https://doi.org/10.48550/arxiv.cond-mat/0506617	text	January 2005
Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet Sachdev, Subir; Ye, Jinwu arXiv https://doi.org/10.48550/arxiv.cond-mat/9212030	text	January 1992
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From Quantum Dynamics to the Canonical Distribution: General Picture and a Rigorous Example Tasaki, Hal arXiv https://doi.org/10.48550/arxiv.cond-mat/9707253	text	January 1997
Lyapunov exponent in quantum mechanics. A phase-space approach Man'ko, V. I.; Mendes, R. Vilela arXiv https://doi.org/10.48550/arxiv.quant-ph/0002049	text	January 2000

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