Interaction - dependent enhancement of the localisation length fortwo interacting particles in a one - dimensional random

We present calculations of the localisation length, 2 , for two interacting particles (TIP) in a one-dimensional random potential, presenting its dependence on disorder, interaction strength U and system size. 2 (U) is computed by a decimation method from the decay of the Green function along the diagonal of nite samples. Innnite sample size estimates 2 (U) are obtained by nite-size scaling. For U = 0 we reproduce approximately the well-known dependence of the one-particle localisation length on disorder while for nite U, we nd that 2 (U) 2 (0) (U) with (U) varying between (0) = 1 and (1) 1:5. We test the validity of various other proposed t functions and also study the problem of TIP in two diierent 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.