Efficient Anderson localization bounds for large multi-particle systems

Abstract

We study multi-particle interactive quantum disordered systems on a polynomially growing countable connected graph ($\mathcal{Z},\mathcal{E}$). The main novelty is to give localization bounds uniform in finite volumes (subgraphs) in ${\mathcal{Z}}^N$ as well as for the whole of ${\mathcal{Z}}^N$. 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 $N$-particle model 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.