Eur. Phys. J. B 7, 451-456 (1999)
https://doi.org/10.1007/s100510050633

Two interacting particles in a disordered chain II: Critical statistics and maximum mixing of the one body states

¹ CEA, Service de Physique de l'État Condensé, Centre d'Études de Saclay, 91191 Gif-sur-Yvette, France
² Institut für Physik, Universität Augsburg, 86135 Augsburg, Germany

Received: 22 May 1998
Revised: 24 August 1998
Accepted: 4 September 1998
Published online: 15 February 1999

Abstract

For two particles in a disordered chain of length L with on-site interaction U, a duality transformation maps the behavior at weak interaction onto the behavior at strong interaction. Around the fixed point of this transformation, the interaction yields a maximum mixing of the one body states. When (the one particle localization length), this mixing results in weak chaos accompanied by multifractal wave functions and critical spectral statistics, as in the one particle problem at the mobility edge or in certain pseudo-integrable billiards. In one dimension, a local interaction can only yield this weak chaos but can never drive the two particle system to full chaos with Wigner-Dyson statistics.