Eigenstate thermalization in dual-unitary quantum circuits: Asymptotics of spectral functions,Physical Review E

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Eigenstate thermalization in dual-unitary quantum circuits: Asymptotics of spectral functions
Physical Review E ( IF 2.2 ) Pub Date : 2021-06-21 , DOI: 10.1103/physreve.103.062133
Felix Fritzsch ₁ , Tomaž Prosen ₁

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The eigenstate thermalization hypothesis provides to date the most successful description of thermalization in isolated quantum systems by conjecturing statistical properties of matrix elements of typical operators in the (quasi)energy eigenbasis. Here we study the distribution of matrix elements for a class of operators in dual-unitary quantum circuits in dependence of the frequency associated with the corresponding eigenstates. We provide an exact asymptotic expression for the spectral function, i.e., the second moment of this frequency resolved distribution. The latter is obtained from the decay of dynamical correlations between local operators which can be computed exactly from the elementary building blocks of the dual-unitary circuits. Comparing the asymptotic expression with results obtained by exact diagonalization we find excellent agreement. Small fluctuations at finite system size are explicitly related to dynamical correlations at intermediate times and the deviations from their asymptotical dynamics. Moreover, we confirm the expected Gaussian distribution of the matrix elements by computing higher moments numerically.

中文翻译：

双幺正量子电路中的本征态热化：谱函数的渐近

本征态热化假说通过推测（准）能量本征基中典型算子的矩阵元素的统计特性，提供了迄今为止对孤立量子系统中热化最成功的描述。在这里，我们研究了双幺正量子电路中一类算子的矩阵元素的分布，这取决于与相应本征态相关的频率。我们为谱函数提供了一个精确的渐近表达式，即这个频率分辨分布的二阶矩。后者是从本地算子之间的动态相关性的衰减中获得的，可以从双幺正电路的基本构建块中精确计算出来。将渐近表达式与通过精确对角化获得的结果进行比较，我们发现非常一致。有限系统大小的小波动与中间时间的动力学相关性及其渐近动力学的偏差明确相关。此外，我们通过数值计算更高的矩来确认矩阵元素的预期高斯分布。

更新日期：2021-06-21

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