The emergence of charged collective modes from a large N extrapolation of the Hubbard model
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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.
11 pages, 2 figures. Corrects an error in a previous version of this work and relates our methods with more conventional and mainstream ones
11 pages, 2 figures. Corrects an error in a previous version of this work and relates our methods with more conventional and mainstream ones