In the past decades, it was recognized that quantum chaos, which is essential for the emergence of statistical mechanics and thermodynamics, manifests itself in the effective description of the eigenstates of chaotic Hamiltonians through random matrix ensembles and the eigenstate thermalization hypothesis. Standard measures of chaos in quantum many-body systems are level statistics and the spectral form factor. In this work, we show that the norm of the adiabatic gauge potential, the generator of adiabatic deformations between eigenstates, serves as a much more sensitive measure of quantum chaos. We are able to detect transitions from non-ergodic to ergodic behavior at perturbation strengths orders of magnitude smaller than those required for standard measures. Using this alternative probe in two generic classes of spin chains, we show that the chaotic threshold decreases exponentially with system size and that one can immediately detect integrability-breaking (chaotic) perturbations by analyzing infinitesimal perturbations even at the integrable point. In some cases, small integrability-breaking is shown to lead to anomalously slow relaxation of the system, exponentially long in system size.

中文翻译：

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绝热本征态变形作为量子混沌的灵敏探针

在过去的几十年中，人们认识到，对于统计力学和热力学的出现必不可少的量子混沌，表现在通过随机矩阵集合和本征态热化假设对混沌哈密顿量本征态的有效描述中。量子多体系统中混沌的标准度量是能级统计和光谱形状因数。在这项工作中，我们证明了绝热规范势的规范，即本征态之间绝热变形的产生者，是对量子混沌更为敏感的度量。我们能够检测到从非遍历行为到遍历行为的转变，其扰动强度比标准测量所需的强度小几个数量级。在两类自旋链中使用这种替代探针，我们表明，混沌阈值随系统规模呈指数下降，并且即使在可积点处，通过分析无穷微扰动，它也可以立即检测出可破坏性（混沌）扰动。在某些情况下，较小的可破坏性被证明会导致系统异常缓慢地松弛，并且系统大小成倍增长。