论文标题
本征状热假说超出标准指标：在小频率下随机矩阵行为的出现
Eigenstate thermalization hypothesis beyond standard indicators: Emergence of random-matrix behavior at small frequencies
论文作者
论文摘要
使用数值精确的对角度化，我们研究了两个不同不可融合量子旋转链的本元基质中局部自旋算子的矩阵元素。我们的重点是该问题在多大程度上可以将本地运营商表示为随机矩阵，尤其是在多大程度上可以将矩阵元素视为不相关的程度。作为主要结果，我们表明在固定能量密度下频带的特征值分布是对矩阵元素之间相关性的敏感探针。我们发现，在矩阵元素与特征态热假说的所有标准指标处于良好一致的尺度上，特征值分布仍然显示出原始操作员的明确签名，这意味着矩阵元素之间的相关性。此外，我们证明在较小的能量尺度上，特征值分布大约假定通用半圆形，表明向随机矩阵行为过渡，尤其是矩阵元素变得不相关。
Using numerical exact diagonalization, we study matrix elements of a local spin operator in the eigenbasis of two different nonintegrable quantum spin chains. Our emphasis is on the question to what extent local operators can be represented as random matrices and, in particular, to what extent matrix elements can be considered as uncorrelated. As a main result, we show that the eigenvalue distribution of band submatrices at a fixed energy density is a sensitive probe of the correlations between matrix elements. We find that, on the scales where the matrix elements are in a good agreement with all standard indicators of the eigenstate thermalization hypothesis, the eigenvalue distribution still exhibits clear signatures of the original operator, implying correlations between matrix elements. Moreover, we demonstrate that at much smaller energy scales, the eigenvalue distribution approximately assumes the universal semicircle shape, indicating transition to the random-matrix behavior, and in particular that matrix elements become uncorrelated.
