Duality Between the Weak and Strong Interaction Limits for Randomly Interacting Fermions
Disordered Systems and Neural Networks
2009-11-07 v4 Strongly Correlated Electrons
High Energy Physics - Theory
Chaotic Dynamics
Nuclear Theory
Abstract
We establish the existence of a duality transformation for generic models of interacting fermions with two-body interactions. The eigenstates at weak and strong interaction U possess similar statistical properties when expressed in the U=0 and U=infinity eigenstates bases respectively. This implies the existence of a duality point U_d where the eigenstates have the same spreading in both bases. U_d is surrounded by an interval of finite width which is characterized by a non Lorentzian spreading of the strength function in both bases. Scaling arguments predict the survival of this intermediate regime as the number of particles is increased.
Cite
@article{arxiv.cond-mat/0109390,
title = {Duality Between the Weak and Strong Interaction Limits for Randomly Interacting Fermions},
author = {Philippe Jacquod and Imre Varga},
journal= {arXiv preprint arXiv:cond-mat/0109390},
year = {2009}
}
Comments
RevTex4, 4 pages, 4 figures. Accepted for publication at Phys. Rev. Lett