Two-body metal-insulator transitions in the Anderson-Hubbard model

TL;DR

This paper reviews recent findings on how interactions affect localization and phase transitions of two particles in disordered lattices, revealing that interactions enhance localization in 2D but do not induce delocalization, and that 3D pairs undergo a standard metal-insulator transition.

Contribution

It provides a comprehensive numerical analysis of two-particle localization, clarifies previous misconceptions about 2D interaction-induced transitions, and maps the complex phase diagram in 3D.

Findings

Interactions exponentially increase pair localization length in 2D without causing delocalization.

In 3D, pairs undergo a metal-insulator transition in the same universality class as noninteracting systems.

The phase diagram shows multiple metallic and insulating phases due to pair state structures.

Abstract

We review our recent results on Anderson localization in systems of two interacting particles coupled by contact interactions. Based on an exact mapping to an effective single-particle problem, we numerically investigate the occurrence of metal-insulator phase transitions for the pair in two- (2D) and three-dimensional (3D) disordered lattices. In two dimensions, we find that interactions cause an exponential enhancement of the pair localization length with respect to its single-particle counterpart, but do not induce a delocalization transition. In particular we show that previous claims of 2D interaction-induced Anderson transitions are the results of strong finite-size effects. In three dimensions we find that the pair undergoes a metal-insulator transition belonging to the same (orthogonal) universality class of the noninteracting model. We then explore the phase diagram in the space of energy E, disorder W and interaction strength U, which reveals a rich and counterintuitive structure, endowed with multiple metallic and insulating phases. We point out that this phenomenon originates from the molecular and scattering-like nature of the pair states available at given energy and disorder strength.