Exact Solvability Of Entanglement For Arbitrary Initial State in an Infinite-Range Floquet System

Harshit Sharma; Udaysinh T. Bhosale

Paper

Exact Solvability Of Entanglement For Arbitrary Initial State in an Infinite-Range Floquet System

Abstract

Sharma and Bhosale [\href{https://journals.aps.org/prb/abstract/10.1103/PhysRevB.109.014412}{Phys. Rev. B \textbf{109}, 014412 (2024)}; \href{https://journals.aps.org/prb/abstract/10.1103/PhysRevB.110.064313}{Phys. Rev. B \textbf{110}, 064313,(2024)}] recently introduced an

-spin Floquet model with infinite-range Ising interactions. There, we have shown that the model exhibits the signatures of quantum integrability for specific parameter values

and

. We have found analytically the eigensystem and the time evolution of the unitary operator for finite values of

up to

qubits. We have calculated the reduced density matrix, its eigensystem, time-evolved linear entropy, and the time-evolved concurrence for the initial states

and

. For the general case

, we have provided sufficient numerical evidences for the signatures of quantum integrability, such as the degenerate spectrum, the exact periodic nature of entanglement dynamics, and the time-evolved unitary operator. In this paper, we have extended these calculations to arbitrary initial state

, such that

and

. Along with that, we have analytically calculated the expression for the average linear entropy for arbitrary initial states. We numerically find that the average value of time-evolved concurrence for arbitrary initial states decreases with

, implying the multipartite nature of entanglement. We numerically show that the values

for Ising strength (

), while for

and

, it deviates from

for arbitrary initial states even though the thermodynamic limit does not exist in our model. This deviation is shown to be a signature of integrability in earlier studies where the thermodynamic limit exist.