Many-Body Delocalization in Strongly Disordered System with Long-Range Interactions: Finite Size Scaling

Many-body localization in a disordered system of interacting spins coupled by the long-range interaction $1/R^{\alpha}$ is investigated combining analytical theory considering resonant interactions and a finite size scaling of exact numerical solutions with a number of spins $N$. The numerical results for a one-dimensional system are consistent with the general expectations of analytical theory for $d$-dimensional system including the absence of localization in the infinite system at $\alpha<2d$ and a universal scaling of a critical energy disordering $W_{c} \propto N^{\frac{2d-\alpha}{d}}$. %The finite size effect on the interaction stimulated delocalization of energy in the ensemble of interacting two level systems in amorphous solids at low temperature is discussed.