Eigenstate Thermalization in Dual Unitary Quantum Circuits

热力学平衡态对孤立量子系统的成功描述引发了这样一个问题：在么正时间演化下，孤立量子系统如何从一个典型的纯初始态热化？本征态热化假说(ETH)用描述宏观观测矩阵元素结构的数学解释来推测答案。尽管数值研究为一般多体量子系统中的ETH提供了强有力的证据，但能够证明给定系统确实满足ETH的分析证据很少。在这个项目中，我建议研究对偶么正量子电路中的本征态热化，并严格地确认ETH及其含义。这样的量子电路为一般的多体量子系统提供了最小的模型，并允许对其显著特征进行分析描述。特别是对偶么正电路模型，它表现出额外的时空对称性，适合于精确的计算，因此是分析证实ETH的极佳候选者。为此，我计划(I)数值研究对偶么正量子电路中的本征态热化，(Ii)建立其量子动力学的解析描述，(Iii)确定局域可观测量的ETH变换，(Iv)研究本征态的纠缠性质，以及(V)将对偶么正量子电路的性质推广到更一般的多体系统。

The successful description of isolated quantum systems by thermodynamic equilibrium states has triggered the question how those systems thermalize from a typical pure initial state under unitary time evolution. The eigenstate thermalization hypothesis (ETH) conjectures an answer in terms of a mathematical ansatz which describes the structure of matrix elements of macroscopic observables. Although numerical studies provide strong evidence for ETH in generic many-body quantum systems, analytical proofs that a given system indeed fulfills ETH are rare. In this project I propose to study eigenstate thermalization in dual-unitary quantum circuits and to rigorously confirm ETH and its implications. Such quantum circuits provide minimal models for generic many-body quantum systems and allow for an analytical description of their prominent features. In particular dual-unitary circuit models, which exhibit an additional space-time symmetry, are suitable for exact calculations and thus are excellent candidates for an analytic confirmation of ETH. To this end I plan to (i) numerically investigate eigenstate thermalization in dual-unitary quantum circuits, (ii) establish an analytical description of their quantum dynamics, (iii) confirm the ETH ansatz for local observables, (iv) study entanglement properties of eigenstates, and (v) extend the properties of dual-unitary quantum circuits to more generic many-body systems.