Abstract: For Anderson localization one-particle models, there exists an exact real-space renormalization procedure (Aoki 1980) that can be used numerically to obtain the statistical properties of the renormalized hopping between two sites separated by a distance L.We will describe the results for the Anderson tight-binding model in dimensions d=2 and d=3.In the localized phase, we obtain the same universality class as the strong disorder phase of the directed polymer in a random medium. At criticality in d=3, the statistics of renormalized hoppings becomes multifractal, in direct correspondence with the multifractality of individual eigenstates. Many-body localization problems can be studied similarly via an exact renormalization procedure in configuration space. For a one-dimensional lattice model of interacting fermions with disorder, we have studied numerically the statistical properties of the renormalized hopping between two configurations separated by a distance L in configuration space (distance being defined as the minimal number of elementary moves to go from one configuration to the other).We find a many-body localization transition at a finite disorder strength, with a localization length diverging as a power law, and with an essential singularity in the delocalized phase.
Anderson localization and many-body localization: Statistics of renormalized hoppings
KIT - Campus South - Wolfgang-Gaede-Str.1
Dr. Cecile Monthus