Exponential asymptotic spin correlations in XY chains

TL;DR

This paper investigates the long-time and long-distance exponential decay of spin correlations in anisotropic XY chains at finite temperature, using numerical methods to extend known results from the isotropic case.

Contribution

It provides a numerical analysis of asymptotic spin correlations in anisotropic XY chains, approximating decay rates without an explicit analytical solution.

Findings

Correlations decay exponentially in space and time.

Numerical results closely match generalized analytical predictions.

Extends understanding from isotropic to anisotropic models.

Abstract

The long-time and long-distance asymptotic behavior of the $x$ spin correlations at finite temperature in an anisotropic spin-1/2 XY chain is determined numerically. The decay of the correlations is exponential in both space and time. Similar exponential decay of correlations was already found earlier in the special case of the isotropic model, where analytical expressions for the decay rates could be derived via a mapping to a different model. While no such mapping is known for the anisotropic model, the asymptotic correlations can be very well approximated by a natural generalization of the known analytic results for the isotropic case.