Localized to extended states transition for two interacting particles in a two-dimensional random potential

TL;DR

This study demonstrates that short-range interactions can induce a transition from localized to extended states for two particles in a 2D random potential, revealing a critical disorder and associated critical exponent.

Contribution

It introduces a numerical method treating interactions as a perturbation to analyze the localization transition in a 2D two-particle system.

Findings

Interaction induces extended states at critical disorder Wc=9.3

Critical exponent for transition is approximately 2.4

No transition observed for non-interacting particles, localization length is halved

Abstract

We show by a numerical procedure that a short-range interaction $u$ induces extended two-particle states in a two-dimensional random potential. Our procedure treats the interaction as a perturbation and solve Dyson's equation exactly in the subspace of doubly occupied sites. We consider long bars of several widths and extract the macroscopic localization and correlation lengths by an scaling analysis of the renormalized decay length of the bars. For $u=1$, the critical disorder found is $W_{\rm c}=9.3\pm 0.2$, and the critical exponent $\nu=2.4\pm 0.5$. For two non-interacting particles we do not find any transition and the localization length is roughly half the one-particle value, as expected.