Scaling the localisation lengths for two interacting particles in one-dimensional random potentials

Using a numerical decimation method, we compute the localisation length λ2 for two onsite interacting particles (TIP) in a one-dimensional random potential. We show that an interaction U>0 does lead to λ2(U)>λ2(0) for not too large U and test the validity of various proposed fit functions for λ2(U). Finite-size scaling allows us to obtain infinite sample size estimates ξ2(U) and we find that ξ2(U)∼ξ2(0)α(U) with α(U) varying between α(0)≈1 and α(1)≈1.5. We observe that all ξ2(U) data can be made to coalesce onto a single scaling curve. We also present results for the problem of TIP in two different random potentials corresponding to interacting electron–hole pairs.