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Spectral statistics across the many-body localization transition

机译：跨多体本地化过渡的光谱统计

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The many-body localization transition (MBLT) between ergodic and many-body localized phases in disordered interacting systems is a subject of much recent interest. The statistics of eigenenergies is known to be a powerful probe of crossovers between ergodic and integrable systems in simpler examples of quantum chaos. We consider the evolution of the spectral statistics across the MBLT, starting with mapping to a Brownian motion process that analytically relates the spectral properties to the statistics of matrix elements. We demonstrate that the flow from Wigner-Dyson to Poisson statistics is a two-stage process. First, a fractal enhancement of matrix elements upon approaching the MBLT from the delocalized side produces an effective power-law interaction between energy levels, and leads to a plasma model for level statistics. At the second stage, the gas of eigenvalues has local interactions and the level statistics belongs to a semi-Poisson universality class. We verify our findings numerically on the XXZ spin chain. We provide a microscopic understanding of the level statistics across the MBLT and discuss implications for the transition that are strong constraints on possible theories.
机译：遍历遍历和无序相互作用系统中的多体本地化阶段之间的多体本地化过渡（MBLT）是最近引起人们关注的主题。在量子混沌的更简单例子中，已知本能统计是遍历遍历和可积系统之间交换的有力工具。我们考虑整个MBLT的光谱统计数据的演变，首先是映射到布朗运动过程，该过程将光谱属性与矩阵元素的统计分析联系起来。我们证明，从维格纳-戴森（Wigner-Dyson）到泊松（Poisson）统计的流程是一个分为两个阶段的过程。首先，当从离域侧接近MBLT时，矩阵元素的分形增强会在能级之间产生有效的幂律相互作用，并导致用于级统计的等离子体模型。在第二阶段，特征值的气体具有局部相互作用，并且水平统计信息属于半泊松普适性类。我们在XXZ自旋链上数字地验证了我们的发现。我们对整个MBLT的级别统计数据有一个微观的了解，并讨论了对过渡的影响，这些影响是对可能理论的严格约束。

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  • 来源
    《Physical review》 |2016年第4期|041424.1-041424.5|共5页
  • 作者

    Maksym Serbyn; Joel E. Moore;

  • 作者单位

    Department of Physics, University of California, Berkeley, California 94720, USA;

    Department of Physics, University of California, Berkeley, California 94720, USA,Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA;

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