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arXiv:2405.15797 · Physical review. B./Physical review. B

Signatures of quantum integrability and exactly solvable dynamics in an infinite-range many-body Floquet spin system

Harshit Sharma, Udaysinh T. Bhosale

Published Aug 14, 2024• 3 citations
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Abstract

In a recent work [Sharma and Bhosale, Phys. Rev. B 109, 014412 (2024)], an $N$-spin Floquet model with infinite-range Ising interaction was introduced. In this paper, we generalize the strength of interaction to $J$, such that the $J=1$ case reduces to the aforementioned work. We show that for $J=1/2$ the model still exhibits integrability only for an even number of qubits. We analytically solve the cases of 6, 8, 10, and 12 qubits, finding the eigensystem, the dynamics of the entanglement for various initial states, and the unitary evolution operator. These quantities exhibit the signature of quantum integrability (QI). For the general case of even $N>12$ qubits, we conjuncture the presence of QI using numerical evidence such as spectrum degeneracy and the exact periodic nature of both the entanglement dynamics and the time-evolved unitary operator. We numerically show the absence of QI for odd $N$ by observing a violation of the signatures of QI. We analytically and numerically find that the maximum value of time-evolved concurrence $({C}_{\mathrm{max}})$ decreases with $N$, indicating the multipartite nature of entanglement. Possible experiments to verify our results are discussed.

DOI
10.1103/physrevb.110.064313

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