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.
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We thank D. Arovas, N. Lindner, D. Podolsky, J. E. Moore, and E. Altman for beneficial discussions. We are grateful to D. Cohen, the administrator of the ATLAS-Technion grid project for his extensive support. S.G. received support from the Simons Investigators Program and the California Institute of Quantum Emulation. N.Y.Y. acknowledges the Miller Institute for Basic Research in Science. A.A. gratefully acknowledges support from the US-Israel Binational Science Foundation Grant No. 2012233 and the Israel Science Foundation and thanks the Aspen Center for Physics, supported by Grant No. NSF-PHY-1066293, for its hospitality.
© 2016 American Physical Society.