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Barišić; Kokalj, Jure; Balog, Ivan; Prelovšek, Peter (2016): Dynamical conductivity and its fluctuations along the crossover to many-body localization. In: Physical Review B, Vol. 94, No. 4, 45126
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Abstract

We present a numerical study of the many-body localization (MBL) phenomenon in the high-temperature limit within an anisotropic Heisenberg model with random local fields. Taking the dynamical spin conductivity sigma(omega) as the test quantity, we investigate the full frequency dependence of sample-to-sample fluctuations and their scaling properties as a function of the system size L <= 28 and the frequency resolution. We identify differences between the general interacting case Delta > 0 and the anisotropy Delta = 0, the latter corresponding to the standard Anderson localization. Except for the extreme MBL case when the relative sample-to-sample fluctuations became large, numerical results allow for the extraction of the low-omega dependence of the conductivity. Results for the dc value sigma(0) indicate a crossover into the MBL regime, i.e., an exponential-like variation with the disorder strength W. For the same regime, our numerical analysis indicates that the low-frequency exponent alpha exhibits a small departure from alpha similar to 1 only.