Absence of two-body delocalization transitions in the two-dimensional Anderson-Hubbard model

TL;DR

This study demonstrates that in a 2D disordered lattice, two particles remain localized regardless of interaction strength, challenging previous claims of an interaction-induced mobility edge and highlighting the absence of two-body delocalization transitions.

Contribution

The paper provides numerical evidence that all pair states are localized in the 2D Anderson-Hubbard model, refuting earlier suggestions of a mobility edge caused by interactions.

Findings

All pair states are localized in infinite 2D lattices.

Previous claims of an interaction-induced mobility edge are biased by finite-size effects.

Localization length shows nonmonotonic behavior with interaction strength.

Abstract

We investigate Anderson localization of two particles moving in a two-dimensional (2D) disordered lattice and coupled by contact interactions. Based on transmission-amplitude calculations for relatively large strip-shaped grids, we find that all pair states are localized in lattices of infinite size. In particular, we show that previous claims of an interaction-induced mobility edge are biased by severe finite-size effects. The localization length of a pair with zero total energy exhibits a nonmonotonic behavior as a function of the interaction strength, characterized by an exponential enhancement in the weakly interacting regime. Our findings also suggest that the many-body mobility edge of the 2D Anderson-Hubbard model disappears in the zero-density limit, irrespective of the (bosonic or fermionic) quantum statistics of the particles.