Efficient Anderson localization bounds for large multi-particle systems

We study multi-particle interactive quantum disordered systems on a polynomially growing countable connected graph. (Z, epsilon) The main novelty is to give localization bounds uniform in finite volumes (subgraphs) in Z(N) as well as for the whole of ZN. Such bounds are proved here by means of a comprehensive fixed-energy multi-particle multiscale analysis. We consider - for the first time in the literature - a discrete N-particlemodel with an infinite-range, sub-exponentially decaying interaction, and establish (1) exponential spectral localization, and (2) strong dynamical localization with sub-exponential rate of decay of the eigenfunction correlators with respect to the natural symmetrized distance in the multi-particle configuration space.