Quantifying Quantum Chaos through Microcanonical Distributions of Entanglement,Physical Review X

当前位置： X-MOL 学术 › Phys. Rev. X › 论文详情

Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)

Quantifying Quantum Chaos through Microcanonical Distributions of Entanglement
Physical Review X ( IF 11.6 ) Pub Date : 2024-07-24 , DOI: 10.1103/physrevx.14.031014
Joaquin F. Rodriguez-Nieva ₁ , Cheryne Jonay ₂ , Vedika Khemani ₂

Affiliation

A characteristic feature of “quantum chaotic” systems is that their eigenspectra and eigenstates display universal statistical properties described by random matrix theory (RMT). However, eigenstates of local systems also encode structure beyond RMT. To capture this feature, we introduce a framework that allows us to compare the ensemble properties of eigenstates in local systems with those of pure random states. In particular, our framework defines a notion of distance between quantum state ensembles that utilizes the Kullback-Leibler divergence to compare the microcanonical distribution of entanglement entropy (EE) of eigenstates with a reference RMT distribution generated by pure random states (with appropriate constraints). This notion gives rise to a quantitative metric for quantum chaos that not only accounts for averages of the distributions but also higher moments. The differences in moments are compared on a highly resolved scale set by the standard deviation of the RMT distribution, which is exponentially small in system size. As a result, the metric can distinguish between chaotic and integrable behaviors and, in addition, quantify and compare the degree of chaos (in terms of proximity to RMT behavior) between two systems that are assumed to be chaotic. We implement our framework in local, minimally structured, Floquet random circuits, as well as a canonical family of many-body Hamiltonians, the mixed-field Ising model (MFIM). Importantly, for Hamiltonian systems, we find that the reference random distribution must be appropriately constrained to incorporate the effect of energy conservation in order to describe the ensemble properties of midspectrum eigenstates. The metric captures deviations from RMT across all models and parameters, including those that have been previously identified as strongly chaotic, and for which other diagnostics of chaos such as level spacing statistics look strongly thermal. In Floquet circuits, the dominant source of deviations is the second moment of the distribution, and this persists for all system sizes. For the MFIM, we find significant variation of the KL divergence in parameter space. Notably, we find a small region where deviations from RMT are minimized, suggesting that “maximally chaotic” Hamiltonians may exist in fine-tuned pockets of parameter space.

中文翻译：

通过纠缠的微正则分布量化量子混沌

“量子混沌”系统的一个特征是它们的特征谱和特征态显示出随机矩阵论（RMT）所描述的普遍统计特性。然而，局部系统的特征态也编码了 RMT 之外的结构。为了捕获这一特征，我们引入了一个框架，允许我们将局部系统中特征态的集合性质与纯随机状态的集合性质进行比较。特别是，我们的框架定义了量子态集合之间距离的概念，它利用 Kullback-Leibler 散度将特征态纠缠熵（EE）的微规范分布与纯随机态（具有适当约束）生成的参考 RMT 分布进行比较。这个概念产生了量子混沌的定量度量，它不仅考虑了分布的平均值，还考虑了更高的矩。矩的差异在 RMT 分布的标准差设置的高分辨率尺度上进行比较，RMT 分布在系统尺寸中呈指数级增长。因此，该指标可以区分混沌行为和可积行为，此外，还可以量化和比较两个被假定为混沌的系统之间的混沌程度（就与 RMT 行为的接近程度而言）。我们在局部的最小结构 Floquet 随机电路以及多体哈密顿量的规范系列中实现我们的框架，即混合场 Ising 模型（MFIM）。重要的是，对于哈密顿系统，我们发现必须适当地约束参考随机分布以包含能量守恒的影响，以便描述中谱特征态的集合特性。该指标捕获所有模型和参数中与 RMT 的偏差，包括那些以前被确定为高度混乱的模型和参数，以及那些其他混沌诊断（如水平间距统计数据）看起来非常热的偏差。在 Floquet 电路中，偏差的主要来源是分布的第二矩，并且对于所有系统大小都存在。对于 MFIM，我们发现参数空间中的 KL 散度存在显着变化。值得注意的是，我们发现一个小区域与 RMT 的偏差最小，这表明“最大混沌”哈密顿量可能存在于微调的参数空间口袋中。

更新日期：2024-07-24

点击分享查看原文

点击收藏

公开下载

阅读更多本刊新发论文本刊介绍/投稿指南