Spin dynamics in the XY model

TL;DR

This paper investigates how entanglement, quantum, and classical correlations evolve in the one-dimensional XY model under a transverse magnetic field, revealing distinct behaviors near quantum phase transitions.

Contribution

It provides a detailed analysis of correlation dynamics in the XY model, highlighting differences between neighbor sites and the impact of anisotropy and magnetic field.

Findings

Quantum phase transition indicated by classical correlation dynamics.

Entanglement behavior varies with magnetic field and neighbor distance.

Quantum and classical correlations evolve differently for nearest and next-nearest neighbors.

Abstract

We study the evolution of entanglement, quantum correlation and classical correlation for the one dimensional XY model in external transverse magnetic field. The system is initialized in the full polarized state along the z axis, after annealing, different sites will become entangled. We study the three kinds of correlation for both the nearest and the next-nearest neighbor sites. We find that for large anisotropy parameter the quantum phase transition can be indicated by the dynamics of classical correlation between the nearest neighbor sites. We find that the dynamics of entanglement for both the nearest and next-nearest neighbor sites show significantly different behaviors with different values of magnetic field. We also find that the evolution of quantum correlation and classical correlation of the nearest neighbor sites are obviously different from those of the next-nearest neighbor sites.