Duality Between the Weak and Strong Interaction Limits for Randomly Interacting Fermions

Details Duality Between the Weak and Strong Interaction Limits for Randomly Interacting Fermions Duality Between the Weak and Strong Interaction Limits for Randomly Interacting Fermions

2001-09-21

arxiv.org/abs/cond-mat/0109390v4

Phys.Rev.Lett. 89 (2002) 134101

Physics

Condensed Matter

Disordered Systems and Neural Networks

RevTex4, 4 pages, 4 figures. Accepted for publication at Phys. Rev. Lett

Scientific paper

10.1103/PhysRevLett.89.134101

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.

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