Violation of Bohigas-Giannoni-Schmit conjecture using an integrable many-body Floquet system

Abstract

Earlier studies have given enough evidence in support of the BGS conjecture, with few exceptions violating it. Here, we provide one more counterexample using a many-body system popularly known as the model of quantum kicked top consisting of $N$ qubits with all-to-all interaction and kicking strength $k=N\pi/2$. We show that it is quantum integrable even though the corresponding semiclassical phase-space is chaotic, thus violating the BGS conjecture. We solve the cases of $N=5$ to $11$ qubits analytically, finding its eigensystem, the dynamics of the entanglement, and the unitary evolution operator. For the general case of $N>11$ qubits, we provide numerical evidence of integrability using degenerate spectrum, and the exact periodic nature of the time-evolved unitary evolution operator and the entanglement dynamics.Comment: 4.5 pages (two-column) + 25 pages (one-column) + 3 figures; Comments are welcom