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

We study a one-dimensional quantum system with an arbitrary number of hard-core particles on the lattice, which are subject to a deterministic attractive interaction as well as a random potential. Our choice of interaction is suggested by the spectral analysis of the XXZ quantum spin chain. The main result concerns a version of high-disorder Fock-space localization expressed here in the configuration space of hard-core particles. The proof relies on an energetically motivated Combes-Thomas estimate and an effective one-particle analysis. As an application, we show the exponential decay of the two-point function in the infinite system uniformly in the particle number.