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Although it is recognized that Anderson localization takes place for allstates at a dimension $d$ less or equal $2$, while delocalization is expectedfor hopping $V(r)$ decreasing with the distance slower or as $r^{-d}$, thelocalization problem in the crossover regime for the dimension $d=2$ andhopping $V(r) \propto r^{-2}$ is not resolved yet. Following earliersuggestions we show that for the hopping determined by two-dimensionalanisotropic dipole-dipole interactions in the presence of time-reversalsymmetry there exist two distinguishable phases at weak and strong disorder.The first phase is characterized by ergodic dynamics and superdiffusivetransport, while the second phase is characterized by diffusive transport anddelocalized eigenstates with fractal dimension less than $2$. The transitionbetween phases is resolved analytically using the extension of scaling theoryof localization and verified numerically using an exact numericaldiagonalization.

Superdiffusion in random two dimensional system with time-reversal symmetry and long-range hopping