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

Using a numerical decimation method, we compute the localisation length lam bda(2), for two onsite interacting particles (TIP) in a one-dimensional ran dom potential. We show that an interaction U > 0 does lead to lambda(2)(U) > lambda(2)(0) for not too large U and test the validity of various propose d fit functions for lambda(2)(U). Finite-size scaling allows us to obtain i nfinite sample size estimates xi(2)(U) and we find that xi(2)(U) similar to xi(2)(0)(alpha(U)) With alpha(U) varying between alpha(0) approximate to 1 and alpha(1) approximate to 1.5. We observe that all xi(2)(U) data can be made to coalesce onto a single scaling curve. We also present results for t he problem of TIP in two different random potentials corresponding to inter acting electron-hole pairs. (C) 1999 Elsevier Science B.V. All rights reser ved.