Adiabatic Eigenstate Deformations as a Sensitive Probe for Quantum Chaos

Pandey, Mohit; Claeys, Pieter W.; Campbell, David; Polkovnikov, Anatoli; Sels, Dries

doi:10.1103/physrevx.10.041017

Cited by 102 publications

(85 citation statements)

References 83 publications

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“…From this perspective, one may question if the nature of the integrability-breaking perturbation plays a role. For instance, the anisotropic Heisenberg model perturbed by a single magnetic impurity located around the centre of the spin chain is known to lead to non-integrable signatures [19][20][21]. We are motivated to answer if indeed, the breaking of integrability induced by such a simple perturbation is enough to render a perfect conductor (ballistic) to a normal conductor (diffusive).…”

Section: Introductionmentioning

confidence: 99%

Many-Body Localization Dynamics from Gauge Invariance

et al. 2018

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We show how lattice gauge theories can display many-body localization dynamics in the absence of disorder. Our starting point is the observation that, for some generic translationally invariant states, the Gauss law effectively induces a dynamics which can be described as a disorder average over gauge superselection sectors. We carry out extensive exact simulations on the real-time dynamics of a lattice Schwinger model, describing the coupling between U(1) gauge fields and staggered fermions. Our results show how memory effects and slow, double-logarithmic entanglement growth are present in a broad regime of parameters-in particular, for sufficiently large interactions. These findings are immediately relevant to cold atoms and trapped ion experiments realizing dynamical gauge fields and suggest a new and universal link between confinement and entanglement dynamics in the many-body localized phase of lattice models.

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Section: Introductionmentioning

confidence: 99%

Many-Body Localization Dynamics from Gauge Invariance

et al. 2018

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“…Even though recent works [21][22][23] derived a generalized expression of FGR to describe diffusive hydrodynamics caused by integrability breaking, the onset of diffusion may still unveil highly nontrivial behavior [24,25]. Additionally, the onset of chaotic/diffusive behavior for fixed weak interactions is not controlled by Fermi's golden rule at small system sizes [26][27][28]. Recent works have also pointed out that the emergence of chaotic/diffusive behavior may not be fully related to the usual measurements of quantum chaos, such as level repulsion [29][30][31] or the eigenstate thermalization hypothesis [32].…”

Section: Introductionmentioning

confidence: 99%

Ballistic-to-diffusive transition in spin chains with broken integrability

Ferreira

Filippone

2020

Phys. Rev. B

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We study the ballistic-to-diffusive transition induced by the weak breaking of integrability in a boundarydriven XXZ spin chain. Studying the evolution of the spin current density J s as a function of the system size L, we show that, accounting for boundary effects, the transition has a nontrivial universal behavior close to the XX limit. It is controlled by the scattering length L * ∝ V −2 , where V is the strength of the integrability-breaking term. In the XXZ model, the interplay of interactions controls the emergence of a transient "quasiballistic" regime at length scales much shorter than L *. This parametrically large regime is characterized by a strong renormalization of the current which forbids a universal scaling, unlike the XX model. Our results are based on matrix product operator numerical simulations and agree with perturbative analytical calculations.

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“…Level statistics have since become one of the predominant diagnostics of quantum chaos. Still, there is a longstanding and still not fully resolved problem of reconciling this notion of quantum chaos with that of classical chaos, defined through Lyapunov exponents of individual trajectories [32][33][34][35][36][37][38][39]. Interestingly, and as we discuss here, these conjectures apply to classical systems as well.…”

Section: Bohigas-giannoni-schmit Conjecture For Classical Systemsmentioning

confidence: 83%

Quantum eigenstates from classical Gibbs distributions

Claeys

Polkovnikov

2021

SciPost Phys.

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We discuss how the language of wave functions (state vectors) and associated non-commuting Hermitian operators naturally emerges from classical mechanics by applying the inverse Wigner-Weyl transform to the phase space probability distribution and observables. In this language, the Schr"odinger equation follows from the Liouville equation, with \hbarℏ now a free parameter. Classical stationary distributions can be represented as sums over stationary states with discrete (quantized) energies, where these states directly correspond to quantum eigenstates. Interestingly, it is now classical mechanics which allows for apparent negative probabilities to occupy eigenstates, dual to the negative probabilities in Wigner’s quasiprobability distribution. These negative probabilities are shown to disappear when allowing sufficient uncertainty in the classical distributions. We show that this correspondence is particularly pronounced for canonical Gibbs ensembles, where classical eigenstates satisfy an integral eigenvalue equation that reduces to the Schr"odinger equation in a saddle-point approximation controlled by the inverse temperature. We illustrate this correspondence by showing that some paradigmatic examples such as tunneling, band structures, Berry phases, Landau levels, level statistics and quantum eigenstates in chaotic potentials can be reproduced to a surprising precision from a classical Gibbs ensemble, without any reference to quantum mechanics and with all parameters (including \hbarℏ) on the order of unity.

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Adiabatic Eigenstate Deformations as a Sensitive Probe for Quantum Chaos

Cited by 102 publications

References 83 publications

Many-Body Localization Dynamics from Gauge Invariance

Many-Body Localization Dynamics from Gauge Invariance

Ballistic-to-diffusive transition in spin chains with broken integrability

Quantum eigenstates from classical Gibbs distributions

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