1:30 pm VIA ZOOM
Momentum occupation number bounds for interacting fermions
I will present rigorous bounds on the momentum occupation numbers in translation invariant free fermion models perturbed by Hubbard interactions and a non-uniform potential. In particular, at finite temperature I will present a bound on the deviation of the momentum occupation numbers from the non-interacting Fermi-Dirac distribution. Among other things, this bound shows that the momentum distribution is very close to that of a low-temperature free Fermi gas in the regime where interaction strength << kT << Fermi energy. This work is motivated by Luttinger’s theorem and related recent work on the momentum space picture 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.