# Mobility edge of two interacting particles in three-dimensional random potentials

## TL;DR

This study explores how two interacting particles in a three-dimensional disordered lattice undergo Anderson transitions, revealing that interactions influence the critical disorder strength but not the universality class of the transition.

## Contribution

It provides a numerical analysis of the mobility edge for two interacting particles, showing the non-monotonic dependence of critical disorder on interaction strength.

## Key findings

- Critical disorder strength varies non-monotonically with interaction strength.
- Interactions do not change the universality class of the Anderson transition.
- Transition occurs in a regime where all single-particle states are localized.

## Abstract

We investigate Anderson transitions for a system of two particles moving in a three-dimensional disordered lattice and subject to on-site (Hubbard) interactions of strength U. The two-body problem is exactly mapped into an effective single-particle equation for the center of mass motion, whose localization properties are studied numerically. We show that, for zero total energy of the pair, the transition occurs in a regime where all single-particle states are localized. In particular the critical disorder strength exhibits a non-monotonic behavior as a function of |U|, increasing sharply for weak interactions and converging to a finite value in the strong coupling limit. Within our numerical accuracy, short-range interactions do not affect the universality class of the transition.