1:30 pm VIA ZOOM
Momentum occupation number bounds for interacting fermions
I will present rigorous bounds on the ground state momentum occupation numbers in free fermion models perturbed by Hubbard interactions and a non-uniform potential. These bounds show that, at weak coupling and/or at low density, the momentum occupation numbers approach their non-interacting values as one moves away from a certain surface in momentum space. In the special case of half-filling on a bipartite lattice, I will also show that this surface coincides with the non-interacting Fermi surface. This work is motivated by Luttinger’s theorem and its recent incarnations, which deal with the momentum space picture of a system of interacting fermions. While those results are interesting, their derivations rely on various assumptions, and such strong results are unlikely to hold for generic models of interacting fermions. In contrast to this situation, the results that I will present hold for concrete models and can serve as a useful starting point for understanding the physics of interacting fermions.