Entanglement in a Time-Dependent Coupled XY Spin Chain in an External Magnetic Field

TL;DR

This paper provides an exact analysis of entanglement dynamics in a time-dependent anisotropic XY spin chain under magnetic fields, revealing non-ergodic behavior, critical phenomena, and parameter-dependent quantum effects at various temperatures.

Contribution

It offers a general solution for the time evolution of entanglement in a driven XY spin chain and explores how system parameters influence quantum correlations over time.

Findings

Entanglement shows non-ergodic and critical behavior at different temperatures.

Asymptotic entanglement depends on the ratio J/h, not individual values.

Quantum effects persist near critical points and zero temperature.

Abstract

We consider an infinite one dimensional anisotropic XY spin chain with a nearest neighbor time-dependent Heisenberg coupling J(t) between the spins in presence of a time-dependent magnetic field h(t). We discuss a general solution for the system and present an exact solution for particular choice of J and h of practical interest. We investigate the dynamics of entanglement for different degrees of anisotropy of the system and at both zero and finite temperatures. We find that the time evolution of entanglement in the system show non-ergodic and critical behavior at zero and finite temperatures and different degrees of anisotropy. The asymptotic behavior of entanglement at the infinite time limit at zero temperature and constant J and h depends only the parameter lambda=J/h rather than the individual values of J and h for all degrees of anisotropy but changes for nonzero temperature. Furthermore, the asymptotic behavior is very sensitive to the initial values of J and h and for particular choices we may create finite asymptotic entanglement regardless of the final values of J and h. The persistence of quantum effects in the system as it evolves and as the temperature is raised is studied by monitoring the entanglement. We find that the quantum effects dominates within certain regions of the kT-lambda space that vary significantly depending on the degree of the anisotropy of the system. Particularly, the quantum effects in the Ising model case persists in the vicinity of both its critical phase transition point and zero temperature as it evolves in time. Moreover, the interplay between the different system parameters to tune and control the entanglement evolution is explored.