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. 
Alexander L. Burin
cond-mat.dis-nn quant-ph