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arXiv · 1602.08257

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

Klaus M. Frahm
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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 $\approx 10^7$ 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 $L_2\sim L_1^2$ 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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Klaus M. Frahm. 2016-05-04. Eigenfunction structure and scaling of two interacting particles in the one-dimensional Anderson model. https://doi.org/10.1140/epjb%2Fe2016-70114-7

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