Abstract

Many-body localization in a disordered system of interacting spins coupled by the long-range interaction 1/R^a is investigated combining analytical theory considering resonant interactions and a finite-size scaling of exact numerical solutions with number of spins N. The numerical results for a one-dimensional system are consistent with the general expectations of analytical theory for a d-dimensional system including the absence of localization in the infinite system at a < 2d and a universal scaling of a critical energy disordering W_{c} ~ N^{(2d-a)/d)}.