Many body localization in the presence of the long range interaction

The localization in a disordered system of N interacting spins coupled by the long range anisotropic interaction 1 Ra is investigated using a finite size scaling in a d 1 dimensional system for N 8 10 12 14 The results supports the absence of localization in the infinite system at a lt 2d and a scaling of a critical energy disordering Wc N2d a in agreement with the analytical theory suggesting the energy delocalization in the subset of interacting resonant pairs of spins as a precursor of the many body delocalization Coauthors: Yuri Kagan Leonid Maksimov Il ya Polishchuk Douglas Natelson Douglas Osheroff