https://doi.org/10.1140/epjb/e2016-70114-7
Regular Article
Eigenfunction structure and scaling of two interacting particles in the one-dimensional Anderson model
Laboratoire de Physique Théorique, Université de
Toulouse, CNRS, UPS, 31062 Toulouse, France
a e-mail: frahm@irsamc.ups-tlse.fr
Received:
25
February
2016
Received in final form:
14
March
2016
Published online:
2
May
2016
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.
Key words: Solid State and Materials
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2016