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

机译：无序相互作用的量子多体系统的能级统计模型

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摘要

We numerically study level statistics of disordered interacting quantum many-body systems. A two-parameter plasma model which controls the level repulsion exponent β and range h of interactions between eigenvalues is shown to reproduce accurately features of level statistics across the transition from the 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 us to obtain a clear picture of the flow of level statistics across the transition. Comparing the spectral form factors of the β-h model and of a system across the ergodic-many-body-localized transition, we show that the range of effective interactions between eigenvalues /; is related to the Thouless time which marks the onset of quantum chaotic behavior of the system. Analysis of level statistics of the random quantum circuit which hosts chaotic and localized phases supports the claim that the 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.
机译：我们在数值上研究了无序相互作用的量子多体系统的水平统计。控制参数的水平排斥指数β和特征值之间的相互作用范围h的两参数等离子体模型显示出可以准确地再现从遍历遍历到多体局部相的过渡过程中的水平统计特征。对高阶间距比的分析表明，所考虑的β-h模型甚至考虑到了长期光谱相关性，并使我们能够清晰地了解过渡过程中电平统计流程。比较遍历人体局部过渡的β-h模型和系统的光谱形式因子，我们表明特征值/的有效相互作用范围;与Thouless时间有关，Thouless时间标志着系统量子混沌行为的开始。对具有混沌和局域相的随机量子电路的能级统计分析表明，β-h模型在遍历遍历和多体局域相之间的过渡中掌握了能级统计的通用特征，这也适用于打破时间反转不变性的系统。

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  • 来源
    《Physical review》 |2020年第10期|104201.1-104201.9|共9页
  • 作者

    Piotr Sierant; Jakub Zakrzewski;

  • 作者单位

    Institute of Theoretical Physics Jagiellonian University in Krakow Łojasiewicza 11 30-348 Kraków Poland Institut de Sciences Fotoniques The Barcelona Institute of Science and Technology 08860 Castelldefels (Barcelona) Spain;

    Institute of Theoretical Physics Jagiellonian University in Krakow Łojasiewicza 11 30-348 Kraków Poland Mark Kac Complex Systems Research Center Jagiellonian University in Krakow 30-348 Kraków Poland;

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