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Anderson localization and many-body localization: Statistics of renormalized hoppings

Anderson localization and many-body localization: Statistics of renormalized hoppings
Venue:

KIT - Campus South - Wolfgang-Gaede-Str.1
Seminar Room 10.01, Bldg. 30.23 (Physikhochhaus)

Date:

08.02.2010

Speaker:

Dr. Cecile Monthus
Service de Physique Théorique
CEA Saclay, Gif-sur-Yvette, France

Time:

14:00

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.