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

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.