The Rosenzweig–Porter model revisited for the three Wigner–Dyson symmetry classes

IF 2.8 2区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY
Tilen Čadež, Dillip Kumar Nandy, Dario Rosa, Alexei Andreanov, Barbara Dietz
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引用次数: 0

Abstract

Interest in the Rosenzweig–Porter model, a parameter-dependent random-matrix model which interpolates between Poisson and Wigner–Dyson (WD) statistics describing the fluctuation properties of the eigenstates of typical quantum systems with regular and chaotic classical dynamics, respectively, has come up again in recent years in the field of many-body quantum chaos. The reason is that the model exhibits parameter ranges in which the eigenvectors are Anderson-localized, non-ergodic (fractal) and ergodic extended, respectively. The central question is how these phases and their transitions can be distinguished through properties of the eigenvalues and eigenvectors. We present numerical results for all symmetry classes of Dyson’s threefold way. We analyzed the fluctuation properties in the eigenvalue spectra, and compared them with existing and new analytical results. Based on these results we propose characteristics of the short- and long-range correlations as measures to explore the transition from Poisson to WD statistics. Furthermore, we performed in-depth studies of the properties of the eigenvectors in terms of the fractal dimensions, the Kullback–Leibler (KL) divergences and the fidelity susceptibility. The ergodic and Anderson transitions take place at the same parameter values and a finite size scaling analysis of the KL divergences at the transitions yields the same critical exponents for all three WD classes, thus indicating superuniversality of these transitions.
针对三个维格纳-戴森对称类别的罗森茨魏格-波特模型再探讨
罗森茨韦格-波特模型是一个依赖参数的随机矩阵模型,它介于泊松统计和维格纳-戴森(WD)统计之间,分别描述了具有规则和混沌经典动力学的典型量子系统特征状态的波动特性。原因是该模型的特征向量在参数范围内分别呈现出安德森定位、非遍历(分形)和遍历扩展。核心问题是如何通过特征值和特征向量的特性来区分这些阶段及其转换。我们给出了戴森三重方式所有对称类的数值结果。我们分析了特征值谱的波动特性,并将其与现有的和新的分析结果进行了比较。在这些结果的基础上,我们提出了短程和长程相关性的特征,作为探索从泊松统计向 WD 统计过渡的措施。此外,我们还从分形维度、库尔巴克-莱布勒(KL)发散和保真度易感性等方面对特征向量的特性进行了深入研究。遍历和安德森转换发生在相同的参数值下,对转换处的 KL 发散进行有限规模缩放分析后发现,所有三个 WD 类别都有相同的临界指数,从而表明这些转换具有超普遍性。
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来源期刊
New Journal of Physics
New Journal of Physics 物理-物理:综合
CiteScore
6.20
自引率
3.00%
发文量
504
审稿时长
3.1 months
期刊介绍: New Journal of Physics publishes across the whole of physics, encompassing pure, applied, theoretical and experimental research, as well as interdisciplinary topics where physics forms the central theme. All content is permanently free to read and the journal is funded by an article publication charge.
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