边缘量子混沌

Alexander Altland, Kun Woo Kim, Tobias Micklitz, Maedeh Rezaei, Julian Sonner, Jacobus J. M. Verbaarschot
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引用次数: 0

摘要

近来,接近基态的多体量子混沌系统的物理学受到了越来越多的关注。这些研究的动力来自于在整个频谱中表现出混沌波动的模型系统的出现(著名的代表是 Sachdev-Ye-Kitaev(SYK)模型),以及同样在接近基态时展开的全息原理物理学。我们将频谱边缘解释为量子临界点,在此结合多种分析和数值方法来识别和全面描述两种不同的普遍性类别:"稀疏 "混沌系统的近边缘物理学和 "密集 "混沌系统的近边缘物理学。两者的区别在于系统的随机参数数与其希尔伯特空间维度之间的比率,在稀疏和致密情况下,两者的比率分别为指数级小或代数级小。这两类系统的主要代表是一般混沌多体模型(稀疏)和不变随机矩阵集合或混沌引力系统(密集)。虽然这两个系列在能量尺度与水平间距相当的情况下具有相同的谱相关性,但状态密度及其在边缘附近的波动是不同的。将 SYK 模型视为稀疏模型的代表,我们结合场论和精确对角法对其边缘谱进行了详细讨论。与此相反,Jackiw-Teitelboim 引力是我们对稠密类的参考模型,对其引力路径积分和随机矩阵理论的分析揭示了它与稀疏类的普遍差异,我们将讨论这些差异对构建全息原理的影响。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Quantum chaos on edge

Quantum chaos on edge
Recently, the physics of many-body quantum chaotic systems close to their ground states has come under intensified scrutiny. Such studies are motivated by the emergence of model systems exhibiting chaotic fluctuations throughout the entire spectrum [the Sachdev-Ye-Kitaev (SYK) model being a renowned representative] as well as by the physics of holographic principles, which likewise unfold close to ground states. Interpreting the edge of the spectrum as a quantum critical point, here we combine a wide range of analytical and numerical methods to the identification and comprehensive description of two different universality classes: the near edge physics of “sparse” and the near edge of “dense” chaotic systems. The distinction lies in the ratio between the number of a system's random parameters and its Hilbert space dimension, which is exponentially small or algebraically small in the sparse and dense case, respectively. Notable representatives of the two classes are generic chaotic many-body models (sparse) and invariant random matrix ensembles or chaotic gravitational systems (dense). While the two families share identical spectral correlations at energy scales comparable to the level spacing, the density of states and its fluctuations near the edge are different. Considering the SYK model as a representative of the sparse class, we apply a combination of field theory and exact diagonalization to a detailed discussion of its edge spectrum. Conversely, Jackiw-Teitelboim gravity is our reference model for the dense class, where an analysis of the gravitational path integral and random matrix theory reveal universal differences to the sparse class, whose implications for the construction of holographic principles we discuss.
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