The emergence of charged collective modes from a large N extrapolation of the Hubbard model

Abstract

We consider a symplectic extrapolation of the Hubbard model of N fold replicated electrons and solve this model exactly in two special cases, at N=infinity in the bosonic sector and for any N on a dimer of two points. At N=infinity we find a multiplet of collective modes that contains neutral spin fluctuations and charged pair fluctuations that are degenerate with each other at zero doping. Our solution of the symplectic model on a dimer of two points for any N interpolates smoothly between N=1 and N=infinity without any visible discontinuity. These results suggest that the inclusion of charged pairing modes in weakly doped antiferromagnets is essential and that an expansion about the N=infinity limit is appropriate in this context.