Interaction-dependent enhancement of the localisation length for two interacting particles in a one-dimensional random potential

We present calculations of the localisation length, lambda(2), for two interacting particles (TIP) in a one-dimensional random potential, presenting its dependence on disorder, interaction strength U and system size. lambda(2)(U) is computed by a decimation method from the decay of the Green function along the diagonal of finite samples. Infinite sample size estimates xi(2)(U) are obtained by finite-size scaling. For U = 0 we reproduce approximately the well-known dependence of the one-particle localisation length on disorder while for finite U, we find that xi(2)(U) similar to xi(2)(0)(beta(U)) With beta(U) varying between beta(0) = 1 and beta(1) approximate to 1.5. We test the validity of various other proposed fit functions and also study the problem of TIP in two different random potentials corresponding to interacting electron-hole pairs. As a check of our method and data, we also reproduce well-known results for the two-dimensional Anderson model without interaction.