Spin transport of weakly disordered Heisenberg chain at infinite temperature

We study the disordered Heisenberg spin chain, which exhibits many-body localization at strong disorder, in the weak to moderate disorder regime. A continued fraction calculation of dynamical correlations is devised, using a variational extrapolation of recurrents. Good convergence for the infinite chain limit is shown. We find that the local spin correlations decay at long times as C∼t-β, whereas the conductivity exhibits a low-frequency power law σ∼ωα. The exponents depict subdiffusive behavior β<1/2,α>0 at all finite disorders and convergence to the scaling result α+2β=1 at large disorders.