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We reinvestigate the behavior of the conductivity of several disordered quantum lattice models at infinite temperature using exact diagonalization. Contrary to the conclusion drawn in a recent investigation of similar quantities in identical systems, we find evidence of a localized regime for strong random fields. We estimate the location of the critical field for the many-body localization transition for the random-field $XXZ$ spin chain, and compare our findings with recent investigations in related systems.
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Berkelbach et al. (2010) studied this question.
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