Two interacting particles in a disordered chain I: Multifractality of the interaction matrix elements |
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Authors: | X Waintal J-L Pichard |
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Institution: | (1) CEA, Service de Physique de l'état Condensé, Centre d'études de Saclay, 91191 Gif-sur-Yvette, France, FR |
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Abstract: | 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.
Received: 17 April 1998 / Accepted: 14 May 1998 |
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Keywords: | PACS 05 45 +b Theory and models of chaotic systems - 72 15 Rn Quantum localization - 71 30 +h Metal-insulator transitions and other electronic transitions |
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