2016/06/30 by Cecile Monthus
Physics and Astronomy · #cond-mat.dis-nn
paper · pdf · doi:10.1088/1742-5468/aa50db
published as J. Stat. Mech. (2016) 123303 · v2=revised version with new sections based on the forward approximation for short-ranged models (17 pages)
arxiv created 2016/11/24 · arxiv updated 2017/01/03
To understand the finite-size-scaling properties of phases transitions in classical and quantum models in the presence of quenched disorder, it has proven to be fruitful to introduce the notion of a finite-size-pseudo-critical point in each disordered sample and to analyze its sample-to-sample fluctuations as a function of the size. For the Many-Body-Localization transition, where very strong eigenstate-to-eigenstate fluctuations have been numerically reported even within a given disordered sample at a given energy density [X. Yu, D. J. Luitz, B. K. Clark, arxiv:1606.01260 and V. Khemani, S. P. Lim, D. N. Sheng, D. A. Huse,arxiv:1607.05756], it seems thus useful to introduce the notion of a finite-size-pseudo-critical point for each individual eigenstate and to study its eigenstate-to-eigenstate fluctuations governed by the correlation length exponent ν. The scaling properties of critical eigenstates are also expected to appear much more clearly if one considers each eigenstate at its finite-size-pseudo-critical point, where it is 'truly critical', while standard averages over eigenstates and samples in the critical region actually see a mixture of states that are effectively either localized or delocalized.