On a random regular graph with intermediate disorder, an initially localized wave packet spreads subdiffusively, with width growing as t^beta where beta = 1 - W/W_AT, for a disorder range where earlier work expected diffusion.
Finite size scaling bounds on many-body localized phase transitions
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abstract
Quantum phase transitions are usually observed in ground states of correlated systems. Remarkably, eigenstate phase transitions can also occur at finite energy density in disordered, isolated quantum systems. Such transitions fall outside the framework of statistical mechanics as they involve the breakdown of ergodicity. Here, we consider what general constraints can be imposed on the nature of eigenstate transitions due to the presence of disorder. We derive Harris-type bounds on the finite-size scaling exponents of the mean entanglement entropy and level statistics at the many-body localization phase transition using several different arguments. Our results are at odds with recent small-size numerics, for which we estimate the crossover scales beyond which the Harris bound must hold.
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cond-mat.dis-nn 1years
2019 1verdicts
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Sub-diffusion in the Anderson model on random regular graph
On a random regular graph with intermediate disorder, an initially localized wave packet spreads subdiffusively, with width growing as t^beta where beta = 1 - W/W_AT, for a disorder range where earlier work expected diffusion.