Two interacting particles in a disordered chain I: Multifractality of the interaction matrix elements

Details Two interacting particles in a disordered chain I: Multifractality of the interaction matrix elements Two interacting particles in a disordered chain I: Multifractality of the interaction matrix elements

1997-06-25

arxiv.org/abs/cond-mat/9706258v3

Eur. Phys. J. B 6, 117-121 (1998)

Physics

Condensed Matter

Strongly Correlated Electrons

First paper of a serie of four, to appear in Eur. Phys. J

Scientific paper

10.1007/s100510050533

For $N$ interacting particles in a one dimensional random potential, we study the structure of the corresponding network in Hilbert space. The states without interaction play the role of the ``sites''. The hopping terms are induced by the interaction. When the one body states are localized, we numerically find that the set of directly connected ``sites'' is multifractal. For the case of two interacting particles, the fractal dimension associated to the second moment of the hopping term is shown to characterize the Golden rule decay of the non interacting states and the enhancement factor of the localization length.

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