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 â107
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 L1â is verified. The enhancement effect of the
two-particle localization length L2â behaving as L2ââŒL12â 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.Comment: 26 pages, 19 png and pdf figures, high quality gif files for panels
of figures 1-4 are available at
http://www.quantware.ups-tlse.fr/QWLIB/tipdisorder1d, final published version
with minor corrections/revisions, addition of Journal reference and DO