Finite temperature transport in disordered Heisenberg chains

Using numerical diagonalization techniques, we explore the effect of local and bond disorder on the finite temperature spin and thermal conductivities of the one dimensional anisotropic spin-1/2 Heisenberg model. High-temperature results for local disorder show that the dc conductivties are finite, apart from the uncorrelated - XY case - where dc transport vanishes. Moreover, at strong disorder, we find finite dc conductivities at all temperatures $T$, except T=0. The low frequency conductivities are characterized by a nonanalytic cusp shape. Similar behavior is found for bond disorder.