Comprehensive proofs of localization in Anderson models with interaction. I. Two-particle localization estimates

TL;DR

This paper extends multi-particle Anderson localization results to models with infinite-range, exponentially decaying interactions, providing detailed proofs and techniques for two-particle localization estimates.

Contribution

It introduces new proofs for localization in interacting disordered quantum systems with infinite-range interactions, building on previous methods.

Findings

Localization proven for models with infinite-range interactions

Extension of existing techniques to more general interaction types

Detailed mathematical proofs of two-particle localization estimates

Abstract

We discuss the techniques and results of the multi-particle Anderson localization theory for disordered quantum systems with nontrivial interaction. After a detailed presentation of the approach developed earlier by Aizenman and Warzel, we extend their results to the models with exponentially decaying, infinite-range interaction.