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

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

Authors

Harshit Sharma, Udaysinh T. Bhosale

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.

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