Eigenfunctions in a two-particle Anderson tight binding model

TL;DR

This paper proves Anderson localisation for a two-particle quantum system on a lattice, demonstrating that disorder and interaction lead to localized eigenfunctions in a multi-dimensional setting.

Contribution

It extends Anderson localisation results to a two-particle model with interaction and IID disorder, a novel advancement in quantum localization theory.

Findings

Localization of eigenfunctions established

Disorder and interaction induce localization

Results applicable to multi-dimensional lattices

Abstract

We establish the phenomenon of Anderson localisation for a quantum two-particle system on a d-dimensional lattice with short-range interaction and in presence of an IID external potential with sufficiently regular marginal distribution.