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

TL;DR

This paper analytically solves the dynamics of an infinite-range Floquet spin system for small N and provides evidence of quantum integrability for larger N through numerical analysis, highlighting periodic entanglement behavior.

Contribution

It offers exact solutions for small systems and conjectures integrability in larger systems based on numerical signatures, advancing understanding of quantum many-body dynamics.

Findings

Exact eigensystem and dynamics for N=5 to 11 qubits

Signatures of quantum integrability in spectral and dynamical properties

Periodic entanglement oscillations in initial unentangled states

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.