Eur. Phys. J. B (2016) 89: 115
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

Abstract

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.