Subsystem eigenstate thermalization hypothesis
Subsystem eigenstate thermalization hypothesis
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DOI：
10.1103/physreve.97.012140
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发表时间：
2018-01-25
影响因子：
2.4
通讯作者：
Liu, Hong
中科院分区：
文献类型：
--
作者：
Dymarsky, Anatoly;Lashkari, Nima;Liu, Hong
受规范典型性定性描述的启发，我们提出了混沌量子系统本征态热化假设（ETH）的一个精确公式。这个公式，我们称之为子系统ETH，是根据子系统的约化密度矩阵。ETH的这种强形式概述了子系统内定义的可观测量集，它保证了本征态热化。我们讨论的限制时，子系统的大小是小的或相当于其补充。在后一种情况下，我们概述的方法来计算领先的体积比例的贡献，冯诺依曼和Renyi纠缠熵。最后，我们在一维伊辛自旋链的情况下提供了数值证据的建议。
Motivated by the qualitative picture of canonical typicality, we propose a refined formulation of the eigenstate thermalization hypothesis (ETH) for chaotic quantum systems. This formulation, which we refer to as subsystem ETH, is in terms of the reduced density matrix of subsystems. This strong form of ETH outlines the set of observables defined within the subsystem for which it guarantees eigenstate thermalization. We discuss the limits when the size of the subsystem is small or comparable to its complement. In the latter case we outline the way to calculate the leading volume-proportional contribution to the von Neumann and Renyi entanglment entropies. Finally, we provide numerical evidence for the proposal in the case of a one-dimensional Ising spin chain.