Dynamical Detection of Level Repulsion in the One-Particle Aubry-André Model

Torres-Herrera, E. J.; Santos, Lea F.

doi:10.3390/condmat5010007

Cited by 8 publications

(7 citation statements)

References 67 publications

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“…(1) remains valid; then, one obtains Eqs. (2) and (4) numerically, a technique widely accepted by the community as the extensive literature reflects [34,35,[48][49][50][51][52][53][54][55][56]. In particular, the importance of correctly estimating the smooth part of the level density has been highlighted before [57].…”

Section: Spectral Statisticsmentioning

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: Spectral Statisticsmentioning

confidence: 99%

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

Corps

Relaño

2021

Phys. Rev. E

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show abstract

“…(1) remains valid; then, one obtains Eqs. ( 2) and (4) numerically, a technique widely accepted by the community as the extensive literature reflects [34,35,[48][49][50][51][52][53][54][55][56]. Very frequently, no information about the functional form of N ( ) is available, and a generic polynomial of a certain degree N ( )…”

Section: Spectral Statisticsmentioning

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.

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“…The study of chaos in many-body quantum systems from a dynamical viewpoint is of great current interest [1][2][3][4][5][6][7][8][9][10][11]. In the traditional approach, which has mainly focused on short-range correlations in the spectrum, level statistics and universal spectral properties through random matrix theory (RMT) [12][13][14] have been popular objects of study.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of spectral correlations in the entanglement Hamiltonian of the Aubry-André-Harper model

2021

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We numerically study the evolution of spectral correlations in the entanglement Hamiltonian (EH) of noninteracting fermions in the Aubry-André-Harper (AAH) model. We analyze the time evolution of the EH spectrum in a nonequilibrium setting by studying several quantities: spectral distribution, level statistics, entanglement entropy, and spectral form factor (SFF) in the context of the delocalization-localization transition in the AAH model. It is observed that the SFF of the entanglement spectrum in the delocalized phase and at the phasetransition point evolves in three time intervals. We make a systematic study of the emergence of these three timescales for various initial states and find that the number of time intervals remains 3 unless the Hamiltonian is tuned in the localized phase or when the initial state is maximally entangled, when there is a featureless time evolution. We find a broad direct correlation between the entanglement entropy and the length of the ramp of the SFF. We also find that in the delocalized phase the spectral correlations are stronger in the center of the spectrum and grow progressively weaker as more and more of the spectrum is considered.

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Dynamical Detection of Level Repulsion in the One-Particle Aubry-André Model

Cited by 8 publications

References 67 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

Dynamics of spectral correlations in the entanglement Hamiltonian of the Aubry-André-Harper model

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