Eur. Phys. J. B 8, 643-652 (1999)
https://doi.org/10.1007/s100510050732

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

¹ Max-Planck-Institut für Physik komplexer Systeme, 01187 Dresden, Germany
² Institut für Physik, Technische Universität, 09107 Chemnitz, Germany

Received: 19 June 1998
Revised: 29 October 1998
Published online: 15 April 1999

Abstract

We present calculations of the localisation length, , for two interacting particles (TIP) in a one-dimensional random potential, presenting its dependence on disorder, interaction strength U and system size. is computed by a decimation method from the decay of the Green function along the diagonal of finite samples. Infinite sample size estimates 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 with varying between and . 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.