Random Matrix Ensemble for the Level Statistics of Many-Body Localization

Buijsman, Wouter; Cheianov, Vadim; Gritsev, Vladimir

doi:10.1103/physrevlett.122.180601

Cited by 59 publications

(67 citation statements)

References 56 publications

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“…In this section we give a detailed comparison of results of the present work with Ref. [57] and comment on differences with earlier works.…”

Section: Figmentioning

confidence: 72%

“…The considered β-h model can be also used to probe the entanglement spectrum in MBL systems [76] or random fractonic circuits [77] as it has been shown to hosts similar, local correlations between energy levels. It would be interesting to relate it to the associated multifractality observed deep The problem of description of level statistics in ergodic-MBL crossover with plasma models has been addressed a few times [53,54,56,57]. In this section we give a detailed comparison of results of the present work with Ref.…”

Section: Figmentioning

confidence: 87%

“…Ref. [57] considers β-Gaussian ensemble as model of level statistics for ergodic-MBL crossover. The only parameter of the model is the level repulsion exponent β, for β = 1 GOE is recovered.…”

Section: Figmentioning

confidence: 99%

“…In particular, the problem of level statistics in this model in the crossover from ergodic to MBL phases has been addressed in [53][54][55][56]. Recently, the β-Gaussian ensemble was considered as a model of level statistics in the ergodic to MBL crossover [57]. It reproduces level correlations only on a single level spacing scale while missing longer-range spectral correlations (see [45] for a detailed comparison also with other models).…”

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confidence: 99%

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Model of level statistics for disordered interacting quantum many-body systems

Sierant

Zakrzewski

2020

Phys. Rev. B

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We numerically study level statistics of disordered interacting quantum many-body systems. A two-parameter plasma model which controls level repulsion exponent β and range h of interactions between eigenvalues is shown to reproduce accurately features of level statistics across the transition from ergodic to many-body localized phase. Analysis of higher order spacing ratios indicates that the considered β-h model accounts even for long range spectral correlations and allows to obtain a clear picture of the flow of level statistics across the transition. Comparing spectral form factors of β-h model and of a system in the ergodic-MBL crossover, we show that the range of effective interactions between eigenvalues h is related to the Thouless time which marks the onset of quantum chaotic behavior of the system. Analysis of level statistics of random quantum circuit which hosts chaotic and localized phases supports the claim that β-h model grasps universal features of level statistics in transition between ergodic and many-body localized phases also for systems breaking time-reversal invariance.Many-body localization (MBL) [1, 2] is a robust phenomenon of ergodicity breaking in disordered interacting quantum many-body systems [3][4][5][6]. It has attracted considerable attention over the last decade, notable findings include an emergent integrability of MBL phase due to the existence of local integrals of motion (LIOMs) [3, 7-10] and an associated unbounded logarithmic growth of the bipartite entanglement entropy after a quench from a separable state [11,12]. A wide regime of subdiffusive transport on the ergodic side of the transition was found [13][14][15]. Signatures of MBL have been observed experimentally in 1D [16,17] and in 2D system [18], however, the stability of MBL in 2D is still debated [19].Spectral statistics of ergodic systems with (without) time reversal invariance follow predictions of Gaussian orthogonal (unitary) ensemble (GOE, GUE, respectively) of random matrices [20,21] while eigenvalues of localized systems are uncorrelated resulting in Poisson statistics (PS). A ratio of consecutive spacings between energy levelswas proposed as a simple probe of the level statistics in [22] with n = 1 and employed in investigation of ergodicity breaking in various settings [23][24][25][26][27][28][29][30]. Higher order spacing ratios (n > 1), studied in [31][32][33][34], are valuable tools to assess properties of level statistics. In contrast to standard measures such as level spacing distribution or number variance they do not require the so called unfolding, i.e. the procedure of setting density of energy levels ρ(E) to unity which can lead to misleading results [35].Recently, an analytical understanding of an appearance of random matrix theory statistics in systems without a clear semiclassical limit have been developed in a periodically driven Ising models [36,37] or in random Floquet circuits [38]. Variants of such systems have been argued to undergo ergodic-MBL transition [39,40].In this work we consider ...

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“…In this section we give a detailed comparison of results of the present work with Ref. [57] and comment on differences with earlier works.…”

Section: Figmentioning

confidence: 72%

Section: Figmentioning

confidence: 87%

Section: Figmentioning

confidence: 99%

mentioning

confidence: 99%

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Model of level statistics for disordered interacting quantum many-body systems

Sierant

Zakrzewski

2020

Phys. Rev. B

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“…[72]. They were, then, extensively applied in numerical studies of manybody localization [72][73][74][75][76][77][78][79][80][81], periodically driven, interacting quantum systems [82], and quantum quenches [83,84]. In Refs.…”

Section: Introductionmentioning

confidence: 99%

Complex Spacing Ratios: A Signature of Dissipative Quantum Chaos

2020

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We introduce a complex-plane generalization of the consecutive level-spacing distribution, used to distinguish regular from chaotic quantum spectra. Our approach features the distribution of complex-valued ratios between nearest-and next-to-nearest neighbor spacings. We show that this quantity can successfully detect the chaotic or regular nature of complex-valued spectra. This is done in two steps. First, we show that, if eigenvalues are uncorrelated, the distribution of complex spacing ratios is flat within the unit circle, whereas random matrices show a strong angular dependence in addition to the usual level repulsion. The universal fluctuations of Gaussian Unitary and Ginibre Unitary universality classes in the large-matrix-size limit are shown to be well described by Wigner-like surmises for small-size matrices with eigenvalues on the circle and on the two-torus, respectively. To study the latter case, we introduce the Toric Unitary Ensemble, characterized by a flat joint eigenvalue distribution on the two-torus. Second, we study different physical situations where nonhermitian matrices arise: dissipative quantum systems described by a Lindbladian, non-unitary quantum dynamics described by nonhermitian Hamiltonians, and classical stochastic processes. We show that known integrable models have a flat distribution of complex spacing ratios whereas generic cases, expected to be chaotic, conform to Random Matrix Theory predictions. Specifically, we were able to clearly distinguish chaotic from integrable dynamics in boundary-driven dissipative spin-chain Liouvillians and in the classical asymmetric simple exclusion process and to differentiate localized from delocalized phases in a nonhermitian disordered many-body system.

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Random matrix model for eigenvalue statistics in random spin systems

Rao

2022

Physica A: Statistical Mechanics and its Applications

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Random Matrix Ensemble for the Level Statistics of Many-Body Localization

Cited by 59 publications

References 56 publications

Model of level statistics for disordered interacting quantum many-body systems

Model of level statistics for disordered interacting quantum many-body systems

Complex Spacing Ratios: A Signature of Dissipative Quantum Chaos

Random matrix model for eigenvalue statistics in random spin systems

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