Exactly solvable dynamics and signatures of integrability in an infinite-range many-body Floquet spin system

Abstract

We study $N$ qubits having infinite-range Ising interaction and subjected to periodic pulse of external magnetic field. We solve the cases of $N=5$ to $11$ qubits analytically, finding its eigensystem, the dynamics of the entanglement for various initial states, and the unitary evolution operator. These quantities shows signatures of quantum integrability. For the general case of $N>11$ qubits, we provide a conjecture on quantum integrability based on the numerical evidences like degenerate spectrum, and the exact periodic nature of the time-evolved unitary evolution operator and the entanglement dynamics. Using linear entropy we show that for class of initial unentangled state the entanglement displays periodically maximum and zero values.

5 pages (two-column) + 26 pages (one-column) + 3 figures. This is a substantially improved version of the previous manuscript, arXiv:2307.14122v1 [quant-ph]. There, we wrongly claimed that the semiclassical limit exists for k=j*pi. In the revised manuscript, the results are interpreted as a spin chain, and it does not have a semiclassical limit. This version is now accepted in Physical Review B

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Cited by in corpus (5)

• Protecting Quantum Information via Many-Body Dynamical Localization
• Signatures of Integrability and Exactly Solvable Dynamics in an Infinite-Range Many-Body Floquet Spin System
• Study of double kicked top: a classical and quantum perspective
• Exact Solvability Of Entanglement For Arbitrary Initial State in an Infinite-Range Floquet System
• Floquet Recurrences in the Double Kicked Top