Numerical results for two interacting particles in a random environment

TL;DR

This paper presents numerical evidence that electron-electron interactions in a one-dimensional random environment can form particle pairs with larger localization lengths, and supports the existence of a localization-delocalization transition for these pairs.

Contribution

It provides numerical analysis of pair formation and localization properties in disordered systems, supporting recent predictions of a transition.

Findings

Pair states have larger localization length than individual particles.

Numerical evidence supports a localization-delocalization transition for pairs.

Interaction matrix analysis and decimation method are effective tools.

Abstract

Much evidence has been collected to date which shows that repulsive electron-electron interaction can lead to the formation of particle pairs in a one-dimensional random energy landscape. The localization length \lambda_2 of these pair states is finite, but larger than the localization length \lambda_1 of the individual particles. After a short review of previous work, we present numerical evidence for this effect based on an analysis of the interaction matrix elements and an application of the decimation method. The results based on the decimation method for a two-dimensional disordered medium support the localization-delocalization transition of pair states predicted recently.