Dyson三对称量子不可积多体系统的随机矩阵行为
Random-matrix behavior of quantum nonintegrable many-body systems with Dyson's three symmetries
摘要：
我们提出了一个一维不可积自旋模型与当地的相互作用，涵盖戴森的三个对称类（类A，AI和AII）的参数值。我们表明，在这些类中的每一个最近邻间距分布同意与随机矩阵相应的对称性。通过研究对角矩阵元素和非对角矩阵元素的标准差之间的比率，我们在数值上发现，它们变得普遍，只取决于对称性的哈密顿量和一个观察，随机矩阵理论预测。这些普适的比率是从孤立的小量子系统的长时间动力学来评估的。
英文摘要：
We propose a one-dimensional nonintegrable spin model with local interactions that covers Dyson's three symmetry classes (classes A, AI, and AII) depending on the values of parameters. We show that the nearest-neighbor spacing distribution in each of these classes agrees with that of random matrices with the corresponding symmetry. By investigating the ratios between the standard deviations of diagonal and off-diagonal matrix elements, we numerically find that they become universal, depending only on symmetries of the Hamiltonian and an observable, as predicted by random matrix theory. These universal ratios are evaluated from long-time dynamics of small isolated quantum systems.
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