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

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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 L 1 is verified. The enhancement effect of the two-particle localization length L 2 behaving as L 2 ~ L 2 1 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.

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  1. Laboratoire de Physique Théorique, Université de Toulouse, CNRS, UPS, 31062, Toulouse, France

    Klaus M. Frahm

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  1. Klaus M. Frahm
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Correspondence to Klaus M. Frahm.

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Frahm, K. Eigenfunction structure and scaling of two interacting particles in the one-dimensional Anderson model. Eur. Phys. J. B 89, 115 (2016). https://doi.org/10.1140/epjb/e2016-70114-7

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  • DOI: https://doi.org/10.1140/epjb/e2016-70114-7

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