Spin dynamics in finite cyclic XY model

TL;DR

This paper investigates the time evolution of a single spin's polarization in a finite cyclic XY model, revealing how wave packets and finite-size effects influence spin dynamics and correlations.

Contribution

It provides a new series expansion for the autocorrelation function in the finite cyclic XY model, enabling detailed analysis of finite-size effects and wave packet dynamics.

Findings

Identification of wave packet behavior in spin polarization

Quantitative description of finite-size revivals and transitions

Approximate expressions for autocorrelation functions

Abstract

Evolution of the z-component of a single spin in the finite cyclic XY spin 1/2 chain is studied. Initially one selected spin is polarized while other spins are completely unpolarized and uncorrelated. Polarization of the selected spin as a function of time is proportional to the autocorrelation function at infinite temperature. Initialization of the selected spin gives rise to two wave packets moving in opposite directions and winding over the circle. We express the correlation function as a series in winding number and derive tractable approximations for each term. This allows to give qualitative explanation and quantitative description to various finite-size effects such as partial revivals and transition from regular to erratic behavior.