Impurity spin relaxation in S=1/2 XX chains

TL;DR

This paper investigates the dynamic autocorrelations of an impurity spin in a S=1/2 XX chain, revealing distinct temperature-dependent decay behaviors and boundary effects through exact numerical calculations.

Contribution

It provides a detailed analysis of impurity spin autocorrelations at various temperatures, including boundary effects, using exact Jordan-Wigner mapping techniques.

Findings

At T=0, correlations decay as power laws.

High T x correlations decay exponentially, z correlations remain power-law.

Boundary impurity correlations follow power laws at all temperatures.

Abstract

Dynamic autocorrelations $<S_i^{\alpha}(t) S_i^{\alpha}>$ (\alpha=x,z) of an isolated impurity spin in a S=1/2 XX chain are calculated. The impurity spin, defined by a local change in the nearest-neighbor coupling, is either in the bulk or at the boundary of the open-ended chain. The exact numerical calculation of the correlations employs the Jordan-Wigner mapping from spin operators to Fermi operators; effects of finite system size can be eliminated. Two distinct temperature regimes are observed in the long-time asymptotic behavior. At T=0 only power laws are present. At high T the x correlation decays exponentially (except at short times) while the z correlation still shows an asymptotic power law (different from the one at T=0) after an intermediate exponential phase. The boundary impurity correlations follow power laws at all T. The power laws for the z correlation and the boundary correlations can be deduced from the impurity-induced changes in the properties of the Jordan-Wigner fermion states.