Two interacting particles in a random potential

TL;DR

This paper investigates how two particles behave in a disordered one-dimensional lattice, revealing a weak logarithmic scaling law for their localization length and showing no significant enhancement due to interactions.

Contribution

The study introduces a new weak Fock space disorder regime and derives a logarithmic scaling law for two-particle localization length.

Findings

Weak logarithmic scaling law derived

No strong enhancement of two-particle localization length observed

Numerical data support theoretical predictions

Abstract

We study the scaling of the localization length of two interacting particles in a one-dimensional random lattice with the single particle localization length. We obtain several regimes, among them one interesting weak Fock space disorder regime. In this regime we derive a weak logarithmic scaling law. Numerical data support the absence of any strong enhancement of the two particle localization length.