Equilibration time in many-body quantum systems

Lezama, Talía L. M.; Torres-Herrera, E. J.; Pérez‐Bernal, F.; Lev, Yevgeny Bar; Santos, Lea F.

doi:10.1103/physrevb.104.085117

Cited by 20 publications

(8 citation statements)

References 74 publications

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“…2(a), we observe a good data collapse extending over the entire range of T shown here. This tentatively suggests T RMT ∝ τ th L for this particular operator, which is also consistent with [97]. Furthermore, in [79], we provide additional results for a nonintegrable XXZ chain with next-nearest neighbor interactions and a local operator exhibiting diffusive transport.…”

supporting

confidence: 81%

Eigenstate Thermalization Hypothesis and Its Deviations from Random-Matrix Theory beyond the Thermalization Time

et al. 2022

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The eigenstate thermalization hypothesis explains the emergence of the thermodynamic equilibrium in isolated quantum many-body systems by assuming a particular structure of the observable's matrix elements in the energy eigenbasis. Schematically, it postulates that off-diagonal matrix elements are random numbers and the observables can be described by random matrix theory (RMT). To what extent a RMT description applies, more precisely at which energy scale matrix elements of physical operators become truly uncorrelated, is, however, not fully understood. We study this issue by introducing a novel numerical approach to probe correlations between matrix elements for Hilbert-space dimensions beyond those accessible by exact diagonalization. Our analysis is based on the evaluation of higher moments of operator submatrices, defined within energy windows of varying width. Considering nonintegrable quantum spin chains, we observe that matrix elements remain correlated even for narrow energy windows corresponding to timescales of the order of thermalization time of the respective observables. We also demonstrate that such residual correlations between matrix elements are reflected in the dynamics of outof-time-ordered correlation functions.

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confidence: 81%

Eigenstate Thermalization Hypothesis and Its Deviations from Random-Matrix Theory beyond the Thermalization Time

et al. 2022

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“…The power-law decay is followed by the correlation hole [66][67][68] which is visible for both quantities but also for the spectral form factor. For C(t) the correlation hole is not apparent but it is present, a deep close up is needed to observe it [69]. We note that also in [69] it was shown how these features depend on both, system size and kind of observable.…”

Section: Dynamics Overviewmentioning

confidence: 75%

Late-time universal distribution functions of observables in one-dimensional many-body quantum systems

Vallejo-Fabila¹,

Torres-Herrera²

2023

Preprint

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We study the probability distribution function of the long-time values of observables being timeevolved by Hamiltonians modeling clean and disordered one-dimensional chains of many spin-1/2 particles. In particular we analyze the return probability and its version for a completely extended initial state, the so-called spectral form factor. We complement our analysis with the spin autocorrelation and connected spin-spin correlation functions, both of interest in experiments with quantum simulators. We show that the distribution function has a universal shape provided the Central Limit Theorem holds. Explicitly, the shape is exponential for the return probability and spectral form factor, meanwhile it is Gaussian for the few-body observables. We also discuss implications over the so-called many-body localization. Remarkably, our approach requires only a single sample of the dynamics, which is quite advantageous for experiments and theory.[1] M. Clusel and E. Bertin, Global fluctuations in physical systems: a subtle interplay between sum and extreme value statistics, Int.

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“…The behaviors of I(t) for all disorder strengths, when the value of c decreases, approaches the ones for uncorrelated disorder [62,84]. Although the repulsion hole is present in RP (t) and I(t), it should be noted that in [92] a careful analysis was performed to show that while for RP (t) the depth of the repulsion hole increases, for I(t) and other observables the depth apparently decreases when the system size increases.…”

mentioning

confidence: 73%

Effects of auto-correlated disorder on the dynamics in the vicinity of the many-body localization transition

Vallejo-Fabila¹,

Torres-Herrera²

2022

Preprint

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Equilibration time in many-body quantum systems

Cited by 20 publications

References 74 publications

Eigenstate Thermalization Hypothesis and Its Deviations from Random-Matrix Theory beyond the Thermalization Time

Eigenstate Thermalization Hypothesis and Its Deviations from Random-Matrix Theory beyond the Thermalization Time

Late-time universal distribution functions of observables in one-dimensional many-body quantum systems

Effects of auto-correlated disorder on the dynamics in the vicinity of the many-body localization transition

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