2014/11/30 by David J. Luitz, Nicolas Laflorencie, Fabien Alet · 1 citation
Physics and Astronomy · #cond-mat.dis-nn #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.91.081103
published as Phys. Rev. B 91, 081103 (2015) · 4+3 pages, 5+3 figures
arxiv created 2014/12/23 · arxiv updated 2015/03/04
We present a large scale exact diagonalization study of the one dimensional spin 1/2 Heisenberg model in a random magnetic field. In order to access properties at varying energy densities across the entire spectrum for system sizes up to L=22 spins, we use a spectral transformation which can be applied in a massively parallel fashion. Our results allow for an energy-resolved interpretation of the many body localization transition including the existence of an extensive many-body mobility edge. The ergodic phase is well characterized by Gaussian orthogonal ensemble statistics, volume-law entanglement, and a full delocalization in the Hilbert space. Conversely, the localized regime displays Poisson statistics, area-law entanglement and non ergodicity in the Hilbert space where a true localization never occurs. We perform finite size scaling to extract the critical edge and exponent of the localization length divergence.