Localization Bounds for Multiparticle Systems

TL;DR

This paper proves that multi-particle quantum systems on a lattice exhibit spectral and dynamical localization under high disorder or weak interactions, with bounds on transition amplitudes decaying exponentially with configuration space distance.

Contribution

It extends localization results to multi-particle systems with finite-range interactions, using fractional moment analysis of Green functions.

Findings

Localization occurs at high disorder or weak interactions.

Transition amplitudes decay exponentially in configuration space.

Results apply uniformly over time.

Abstract

We consider the spectral and dynamical properties of quantum systems of $n$ particles on the lattice $\Z^d$, of arbitrary dimension, with a Hamiltonian which in addition to the kinetic term includes a random potential with iid values at the lattice sites and a finite-range interaction. Two basic parameters of the model are the strength of the disorder and the strength of the interparticle interaction. It is established here that for all $n$ there are regimes of high disorder, and/or weak enough interactions, for which the system exhibits spectral and dynamical localization. The localization is expressed through bounds on the transition amplitudes, which are uniform in time and decay exponentially in the Hausdorff distance in the configuration space. The results are derived through the analysis of fractional moments of the $n$-particle Green function, and related bounds on the eigenfunction correlators.