Interaction induced delocalization of two particles: large system size calculations and dependence on interaction strength

The localization length L-2 of two interacting particles in a one-dimension al disordered system is studied for very large system sizes by an efficient and accurate variant of the Green function method. The numerical results ( at the band center) can be well described by the functional form L-2 = L-1[ 0.5 + c(U)L-1] where L-1 is the one-particle localization length and the co efficient c(U) approximate to 0.074 \U\/(1+ \U\) depends on the strength U of the on-site Hubbard interaction. The Breit-Wigner width or equivalently the (inverse) life time of non-interacting pair states is analytically calc ulated for small disorder and taking into account the energy dependence of the one-particle localization length. This provides a consistent theoretica l explanation of the numerically found U-dependence of c(U).