https://doi.org/10.1007/s100510050533
Two interacting particles in a disordered chain I: Multifractality of the interaction matrix elements
CEA, Service de Physique de l'État Condensé,
Centre d'Études de Saclay, 91191 Gif-sur-Yvette, France
Corresponding author: a pichard@spec.saclay.cea.fr
Received:
17
April
1998
Accepted:
14
May
1998
Published online: 15 November 1998
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.
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
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 1998
