Localization properties of two interacting electrons in a disordered quasi one-dimensional potential

We study the transport properties of two electrons in a quasi one-dimensional disordered wire. The electrons are subject to both a disorder potential and a short range two-body interaction. Using the approach developed by Iida et al (1990 Ann. Phys., NY 200 219), the supersymmetry technique and a suitable truncation of Hilbert space, we work out the two-point correlation function in the framework of a nonlinear σ model. We study the loop corrections to arbitrary order. We obtain a remarkably simple and physically transparent expression for the change of the localization length caused by the two-body interaction