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

We present calculations of the localisation length, λ2, for two interacting particles (TIP) in a one-dimensional random potential, presenting its dependence on disorder, interaction strength U and system size. λ2(U) is computed by a decimation method from the decay of the Green function along the diagonal of finite samples. Infinite sample size estimates ξ2(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 ξ2(U) ∼ ξ2(0) with β(U) varying between β(0) = 1 and β(1) ≈ 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. 71.55.Jv, 72.15.Rn, 71.30.+h Typeset using REVTEX