Crossover effects in the random exchange spin-1/2 antiferromagnetic chain

The random antiferromagnetic spin-1/2 XX and XXZ chain is studied numerically for varying strength of the disorder, using exact diagonalization and stochastic series expansion methods. The spin-spin correlation function as well as the stiffness display a clear crossover from the pure behavior (no disorder) to the infinite randomness fixed point or random singlet behavior predicted by the the real space renormalization group. The crossover length scale is shown to diverge as $\xi\sim{\mathcal D}^{-\gamma}$, where ${\mathcal D}$ is the variance of the random bonds. Our estimates for the exponent $\gamma$ agrees well within the error bars with the one for the localization length exponent emerging within an analytical bosonization calculation. Exact diagonalization and stochastic series expansion results for the string correlation function are also presented.