arXiv:cond-mat/0109390·v4·cond-mat.dis-nn
Duality Between the Weak and Strong Interaction Limits for Randomly Interacting Fermions
Philippe Jacquod (1) · Imre Varga (2) ((1) Universiteit Leiden, The Netherlands, (2) Philipps-Universitaet Marburg, Germany)
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.
Comments: RevTex4, 4 pages, 4 figures. Accepted for publication at Phys. Rev. Lett