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Simone Warzel

Low-energy Fock-space localization for attractive hard-core particles in disorder

Abstract:Imbrie's works notwithstanding, complete mathematical proofs of many-body localization for  many particle systems remain a challenge.After providing a short overview of known results, I will present a new paper (jointly  with V. Beaud). It concerns one-dimensional  quantum systems of an arbitrary number of hard-core particles on the lattice, which are subject to a deterministic attractive interaction as well as a random potential. The choice of the interaction is motivated by the spectral analysis of the XXZ quantum spin chain. A version of high-disorder Fock-space localization expressed in the configuration space of hard-core particles is proven for energies below the two-cluster threshold. As a consequence, I will show the exponential decay of the two-point function of low-energy eigenfunction uniformly in the system size and the particle number.

Technically, the proof is based on older works (joint with M. Aizenman concerning complete $ n $-particle localization) and some energetic estimates.