Signatures of Integrability and Exactly Solvable Dynamics in an Infinite-Range Many-Body Floquet Spin System

TL;DR

This paper investigates an infinite-range Floquet spin system, revealing integrability signatures for even numbers of qubits at specific interaction strengths, and demonstrates how entanglement dynamics reflect these integrability properties.

Contribution

It analytically and numerically characterizes integrability in an extended Floquet spin model, identifying conditions for integrability and analyzing entanglement behavior across different system sizes.

Findings

Integrability signatures are present for even N at J=1/2.

Maximum concurrence decreases with increasing N.

Odd N systems do not exhibit integrability signatures.

Abstract

In a recent work Sharma and Bhosale [Phys. Rev. B, 109, 014412 (2024)], $N$-spin Floquet model having infinite range Ising interaction was introduced. In this paper, we generalized the strength of interaction to $J$, such that $J=1$ case reduces to the aforementioned work. We show that for $J=1/2$ the model still exhibits integrability for an even number of qubits only. We analytically solve the cases of $6$, $8$, $10$, and $12$ qubits, finding its eigensystem, dynamics of 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 the numerical evidences 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 ($C_{\mbox{max}}$) decreases with $N$, indicating the multipartite nature of entanglement. Possible experiments to verify our results are discussed.