Eigenfunction structure and scaling of two interacting particles in the one-dimensional Anderson model

The localization properties of eigenfunctions for two interacting particles in the one-dimensional Anderson model are studied for system sizes up to N = 5000 sites corresponding to a Hilbert space of dimension ≈107 using the Green function Arnoldi method. The eigenfunction structure is illustrated in position, momentum and energy representation, the latter corresponding to an expansion in non-interacting product eigenfunctions. Different types of localization lengths are computed for parameter ranges in system size, disorder and interaction strengths inaccessible until now. We confirm that one-parameter scaling theory can be successfully applied provided that the condition of N being significantly larger than the one-particle localization length L1 is verified. The enhancement effect of the two-particle localization length L2 behaving as L2 ~ L21 is clearly confirmed for a certain quite large interval of optimal interactions strengths. Further new results for the interaction dependence in a very large interval, an energy value outside the band center, and different interaction ranges are obtained.