Exact Diag. Study of the 1D 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 $\Delta$ between $-1/2$ and $1$, while the superfluidity persists to finite disorder strength for $-1 < \Delta < -1/2$ and then undergoes a Kosterlitz-Thouless type transition.