Characterizing eigenstate thermalization via measures in the Fock space of operators.
Characterizing eigenstate thermalization via measures in the Fock space of operators.
复制标题
通过算子福克空间中的测量来表征本征态热化。
作者：
P. Hosur;X. Qi
本征态热化假设（ETH）试图弥合孤立量子系统的量子力学和统计力学描述之间的差距。在这里，我们通过将规则晶格上的一般相互作用量子系统映射到生活在高维图上的单个粒子上，定义了ETH在各种制度下工作的无偏度量。通过数值分析ETH的行为在不可积伊辛模型的偏差，我们提出了一个数量，我们称之为n-重量民主地表征的平均偏差为所有运营商居住在一个给定数量的网站，无论其空间结构。它似乎有一个简单的标度形式，我们猜想这对所有不可积系统都成立。一个密切相关的量，我们称之为n-similability，告诉我们如何以及两个国家可以区分，如果只测量n-site运营商。沿着的方式，我们发现，复杂的运营商平均比简单的在区分相邻的本征态，相反，由ETH的通常声明，少体（多体）运营商获得相同（不同）的期望值在有限的能量密度附近的本征态的天真的直觉。最后，我们勾勒出启发式的论点，ETH起源于简单的运营商之间的量子态的系统，特别是当状态受到约束，如相对于本地哈密顿量大致固定的能量有限的能力。
The eigenstate thermalization hypothesis (ETH) attempts to bridge the gap between quantum mechanical and statistical mechanical descriptions of isolated quantum systems. Here, we define unbiased measures for how well the ETH works in various regimes, by mapping general interacting quantum systems on regular lattices onto a single particle living on a high-dimensional graph. By numerically analyzing deviations from ETH behavior in the nonintegrable Ising model, we propose a quantity that we call the n-weight to democratically characterize the average deviations for all operators residing on a given number of sites, irrespective of their spatial structure. It appears to have a simple scaling form, which we conjecture to hold true for all nonintegrable systems. A closely related quantity, which we term the n-distinguishability, tells us how well two states can be distinguished if only n-site operators are measured. Along the way, we discover that complicated operators on average are worse than simple ones at distinguishing between neighboring eigenstates, contrary to the naive intuition created by the usual statements of the ETH that few-body (many-body) operators acquire the same (different) expectation values in nearby eigenstates at finite energy density. Finally, we sketch heuristic arguments that the ETH originates from the limited ability of simple operators to distinguish between quantum states of a system, especially when the states are subject to constraints such as roughly fixed energy with respect to a local Hamiltonian.