Spin correlation functions in random-exchange s=1/2 XXZ chains

TL;DR

This paper investigates how disorder affects spin correlation decay in the 1D spin-1/2 XXZ chain at zero temperature, revealing power-law and exponential decay behaviors depending on the type of correlation and disorder strength.

Contribution

It provides numerical analysis of disorder effects on spin correlations in the XXZ chain, highlighting the transition from power-law to exponential decay with disorder.

Findings

Longitudinal correlations decay as a power law with variable exponents.

Transverse correlations transition from power-law to exponential decay with disorder.

Disorder influences the decay behavior differently for longitudinal and transverse correlations.

Abstract

The decay of (disorder-averaged) static spin correlation functions at T=0 for the one-dimensional spin-1/2 XXZ antiferromagnet with uniform longitudinal coupling $J\Delta$ and random transverse coupling $J\lambda_i$ is investigated by numerical calculations for ensembles of finite chains. At $\Delta=0$ (XX model) the calculation is based on the Jordan-Wigner mapping to free lattice fermions for chains with up to N=100 sites. At $\Delta \neq 0$ Lanczos diagonalizations are carried out for chains with up to N=22 sites. The longitudinal correlation function $<S_0^z S_r^z>$ is found to exhibit a power-law decay with an exponent that varies with $\Delta$ and, for nonzero $\Delta$, also with the width of the $\lambda_i$-distribution. The results for the transverse correlation function $<S_0^x S_r^x>$ show a crossover from power-law decay to exponential decay as the exchange disorder is turned on.