Interaction-Induced Delocalization of Two Particles in a Random Potential: Scaling Properties

Abstract

The localization length ${\xi }_2$ for coherent propagation of two interacting particles in a random potential is studied using a novel and efficient numerical method. We find that the enhancement of ${\xi }_2$ over the one-particle localization length ${\xi }_1$ satisfies the scaling relation ${\xi }_2/{\xi }_1=f\left(u/{\Delta }_{\xi }\right)$, where $u$ is the interaction strength and ${\Delta }_{\xi }$ the level spacing of a wire of length ${\xi }_1$. The scaling function $f$ is linear over the investigated parameter range. This implies that ${\xi }_2$ increases faster with $u$ than previously predicted. We also study a novel mapping of the problem to a banded-random-matrix model.