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 conductivities 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 at $T=0$. The low-frequency conductivities are characterized by a nonanalytic cusp shape. Similar behavior is found for bond disorder.