Scrambling Dynamics across a Thermalization-Localization Quantum Phase Transition

Sahu, Subhayan; Xu, Shenglong; Swingle, Brian

doi:10.1103/physrevlett.123.165902

Cited by 47 publications

(27 citation statements)

References 71 publications

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“…(For the physics of the MBL phase, see e.g. [71,72,73,74]; for OTOC calculations see [75,76,77,78,79].) As W is lowered, ergodic phase expands from the center of the spectrum, and gradually the system becomes ergodic except for a small region at low and high energy regions.…”

Section: Xxz Spin Chainmentioning

confidence: 99%

Quantum Lyapunov spectrum

Gharibyan

Hanada

Swingle

et al. 2019

J. High Energ. Phys.

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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 manybody 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.

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Section: Xxz Spin Chainmentioning

confidence: 99%

Quantum Lyapunov spectrum

Gharibyan

Hanada

Swingle

et al. 2019

J. High Energ. Phys.

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“…As motivated from the perspective of operator scrambling in strongly coupled field theories with a gravity dual [9][10][11][12][13], they have been shown to exhibit exponential growth in many field theories [14][15][16][17][18][19][20]. Moreover, OTOCs spread (in general) ballistically in space with a "butterfly velocity" quantifying the speed of scrambling, which has been also found in non-relativistic lattice systems [21][22][23][24][25][26][27][28][29][30]. Such ballistic spreading is to be expected in systems with well-defined quasiparticles [31], but even strongly coupled systems without quasiparticles exhibit a well-defined butterfly velocity.…”

Section: Introductionmentioning

confidence: 99%

Many-body chaos near a thermal phase transition

Schuckert

Knap

2019

SciPost Phys.

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We study many-body chaos in a (2+1)D relativistic scalar field theory at high temperatures in the classical statistical approximation, which captures the quantum critical regime and the thermal phase transition from an ordered to a disordered phase. We evaluate out-of-time ordered correlation functions (OTOCs) and find that the associated Lyapunov exponent increases linearly with temperature in the quantum critical regime, and approaches the non-interacting limit algebraically in terms of a fluctuation parameter. OTOCs spread ballistically in all regimes, also at the thermal phase transition, where the butterfly velocity is maximal. Our work contributes to the understanding of the relation between quantum and classical many-body chaos and our method can be applied to other field theories dominated by classical modes at long wavelengths.

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“…At first sight, this suggests a simple description. However, capturing both the microscopic details of short-time thermalization as well as the crossover to late-time hydrodynamics remains an open challenge [7][8][9][10][11][12][13][14][15]. Indeed, despite nearly a century of progress, no general framework exists for perhaps the simplest question: How does one derive a classical diffusion coefficient from a quantum many-body Hamiltonian?…”

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confidence: 99%

Emergent Hydrodynamics in Nonequilibrium Quantum Systems

Machado

White

et al. 2020

Phys. Rev. Lett.

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A tremendous amount of recent attention has focused on characterizing the dynamical properties of periodically driven many-body systems. Here, we use a novel numerical tool termed "density matrix truncation" (DMT) to investigate the late-time dynamics of large-scale Floquet systems. We find that DMT accurately captures two essential pieces of Floquet physics, namely, prethermalization and late-time heating to infinite temperature. Moreover, by implementing a spatially inhomogeneous drive, we demonstrate that an interplay between Floquet heating and diffusive transport is crucial to understanding the system's dynamics. Finally, we show that DMT also provides a powerful method for quantitatively capturing the emergence of hydrodynamics in static (undriven) Hamiltonians; in particular, by simulating the dynamics of generic, large-scale quantum spin chains (up to L ¼ 100), we are able to directly extract the energy diffusion coefficient.

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Scrambling Dynamics across a Thermalization-Localization Quantum Phase Transition

Cited by 47 publications

References 71 publications

Quantum Lyapunov spectrum

Quantum Lyapunov spectrum

Many-body chaos near a thermal phase transition

Emergent Hydrodynamics in Nonequilibrium Quantum Systems

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