Random-matrix behavior of quantum nonintegrable many-body systems with Dyson's three symmetries. (arXiv:1901.02119v2 [cond-mat.stat-mech] UPDATED)

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.

Article web page: