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

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.

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 DOI

References in corpus (4)

• Observation of many-body localization of interacting fermions in a quasi-random optical lattice
• Ulam method for the Chirikov standard map
• Interaction-induced connectivity of disordered two-particle states
• Freed by interaction kinetic states in the Harper model

Cited by in corpus (19)

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• Anderson localization of composite particles
• Multifractality of correlated two-particle bound states in quasiperiodic chains
• Interaction-Induced Weakening of Localization in Few-Particle Disordered Heisenberg Chains
• Mobility edge of two interacting particles in three-dimensional random potentials
• Absence of two-body delocalization transitions in the two-dimensional Anderson-Hubbard model
• Two-body mobility edge in the Anderson-Hubbard model in three dimensions: Molecular versus scattering states
• Logarithmic expansion of many-body wave packets in random potentials
• Chaotic delocalization of two interacting particles in the classical Harper model
• Two particles on a chain with disordered interaction: Localization and dissociation of bound states and mapping to chaotic billiards
• Two-body metal-insulator transitions in the Anderson-Hubbard model
• Universal fluctuations of localized two interacting particles in one dimension
• Deconfinement of classical Yang-Mills color fields in a disorder potential
• 2D Anderson Localization and KPZ sub-Universality Classes : sensitivity to boundary conditions and insensitivity to symmetry classes