Average entanglement entropy of midspectrum eigenstates of quantum-chaotic interacting Hamiltonians
Average entanglement entropy of midspectrum eigenstates of quantum-chaotic interacting Hamiltonians
复制标题
量子混沌相互作用哈密顿量的中谱本征态的平均纠缠熵
DOI：
10.1103/physreve.107.064119
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发表时间：
2023
影响因子：
2.4
通讯作者：
Rigol, M.
中科院分区：
文献类型：
--
作者：
Kliczkowski, M.;Świętek, R.;Vidmar, L.;Rigol, M.
量子-混沌相互作用哈密顿量的中谱本征态的平均纠缠熵与随机纯态的平均纠缠熵在多大程度上一致是近年来引起广泛关注的问题。虽然有大量的证据表明，主导（体积法）条款是相同的，哪些以及如何子主导条款之间的差异不太清楚。在这里，我们进行了国家的最先进的完全精确对角化计算干净的自旋1/2 XYZ和XXZ链与可积性破缺项，以解决这个问题，在缺乏和存在的对称性，分别。我们首先引入最大混沌政权的概念，适合于完全精确的对角化计算的链尺寸，作为汉密尔顿参数的政权，其中能级间距比，本征态系数的分布，和纠缠熵最接近随机矩阵理论的预测。在此范围内，我们对中谱本征态平均纠缠熵的次主导项进行了有限尺度尺度分析。我们发现的迹象表明，为，negativecorrection的幅度仅略大于随机纯态的预测。对于有限的，遵循唯象的方法，我们推导出一个简单的表达式，它描述了随机纯态的预测偏差的数值计算依赖性。
To which degree the average entanglement entropy of midspectrum eigenstates of quantum-chaotic interacting Hamiltonians agrees with that of random pure states is a question that has attracted considerable attention in the recent years. While there is substantial evidence that the leading (volume-law) terms are identical, which and how subleading terms differ between them is less clear. Here we carry out state-of-the-art full exact diagonalization calculations of clean spin-1/2 XYZ and XXZ chains with integrability breaking terms to address this question in the absence and presence ofsymmetry, respectively. We first introduce the notion of maximally chaotic regime, for the chain sizes amenable to full exact diagonalization calculations, as the regime in Hamiltonian parameters in which the level spacing ratio, the distribution of eigenstate coefficients, and the entanglement entropy are closest to the random matrix theory predictions. In this regime, we carry out a finite-size scaling analysis of the subleading terms of the average entanglement entropy of midspectrum eigenstates when different fractionsof the spectrum are included in the average. We find indications that, for, the magnitude of the negativecorrection is only slightly greater than the one predicted for random pure states. For finite, following a phenomenological approach, we derive a simple expression that describes the numerically observeddependence of thedeviation from the prediction for random pure states.