Exact-diagonalization study of the one-dimensional disordered XXZ model

We investigate the one-dimensional quantum XXZ model in the presence of diagonal disorder. Recently the model has been analyzed with the help of field-theoretical renormalization-group methods, and a phase diagram has been predicted. We study the model with exact diagonalization techniques up to chain lengths of 16 sites. Using finite-size scaling methods we estimate critical exponents and the phase diagram and find reasonably good agreement with the field-theoretical results, namely, that any amount of disorder destroys the superfluidity for XXZ anisotropy Δ between -1/2 and 1, while the superfluidity persists to finite disorder strength for -1<Δ<-1/2 and then undergoes a Kosterlitz-Thouless-type transition