Entanglement in a time-dependent coupled XY spin chain in an external magnetic field

Abstract

We consider an infinite one-dimensional anisotropic $\mathit{XY}$ 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 shows nonergodic 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 $\ensuremath{\lambda}=J/h$ 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 dominate within certain regions of the $\mathit{kT}$-$\ensuremath{\lambda}$ space that vary significantly depending on the degree of the anisotropy of the system. Particularly, the quantum effects in the Ising model case persist 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.