Breakdown of ergodicity in quantum systems: from solids to synthetic matter

Pepper, M.; Pal, Arijeet; Papić, Zlatko; Schneider, Ulrich; Simon, Steven H.

doi:10.1098/rsta.2017.0264

Cited by 2 publications

(2 citation statements)

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“…The last years have witnessed a revival of the interest in quantum chaos and spectral statistics due to the yet to uncover exotic features of many-body quantum systems without a semiclassical analog [1]. A closely related concept is that of quantum integrability, which is also present in many current research topics, from nonequilibrium dynamics and thermalization [2] to many-body localization and condensed matter [3].…”

Section: Introductionmentioning

confidence: 99%

Long-range level correlations in quantum systems with finite Hilbert space dimension

Corps

Relaño

2021

Phys. Rev. E

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We study the spectral statistics of quantum systems with finite Hilbert spaces. We derive a theorem showing that eigenlevels in such systems cannot be globally uncorrelated, even in the case of fully integrable dynamics, as a consequence of the unfolding procedure. We provide an analytic expression for the power spectrum of the δ n statistic for a model of intermediate statistics with level repulsion but independent spacings, and we show both numerically and analytically that the result is spoiled by the unfolding procedure. Then, we provide a simple model to account for this phenomenon, and test it by means of numerics on the disordered X X Z chain, the paradigmatic model of many-body localization, and the rational Gaudin-Richardson model, a prototypical model for quantum integrability.

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Section: Introductionmentioning

confidence: 99%

Long-range level correlations in quantum systems with finite Hilbert space dimension

Corps

Relaño

2021

Phys. Rev. E

View full text Add to dashboard Cite

show abstract

“…The last years have witnessed a revival of the interest in quantum chaos and spectral statistics due to the yet to uncover exotic features of many-body quantum systems without a semiclassical analogue [1]. A closely related concept is that of quantum integrability, which is also present in many current research topics, from non-equilibrium dynamics and thermalization [2] to many-body localization and condensed matter [3].…”

Section: Introductionmentioning

confidence: 99%

Long-range level correlations in quantum systems with finite Hilbert space dimension

Corps,

Relaño

2020

Preprint

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We study the spectral statistics of quantum systems with finite Hilbert spaces. We derive a theorem showing that eigenlevels in such systems cannot be globally uncorrelated, even in the case of fully integrable dynamics, as a consequence of the unfolding procedure. We provide an analytic expression for the power spectrum of the statistic for a model of intermediate statistics with level repulsion but independent spacings, and we show both numerically and analytically that the result is spoiled by the unfolding procedure. Then, we provide a simple model to account for this phenomenon, and test it by means of numerics on the disordered XXZ chain, the paradigmatic model of many-body localization, and the rational Gaudin-Richardson model, a prototypical model for quantum integrability.

show abstract

Breakdown of ergodicity in quantum systems: from solids to synthetic matter

Abstract: One contribution of 10 to a discussion meeting issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'.

Cited by 2 publications

References 23 publications

Long-range level correlations in quantum systems with finite Hilbert space dimension

Long-range level correlations in quantum systems with finite Hilbert space dimension

Long-range level correlations in quantum systems with finite Hilbert space dimension

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