The paradigmatic Hubbard model for strong correlations in quantum matter is that of electrons hopping on a lattice between nearest neighbors but paying the energy cost U anytime they doubly occupy the same site. However, due to the fact that the potential and kinetic terms do not commute, this simple model remains unsolved in any dimension exceeding unity. In this talk I'll review some of the previous results on Hubbard model in 1d and 2d. Then I'll introduce the extended orbital Hatsugai-Kohmoto(HK) Models which include non-commutativity between potential and the kinetic energy terms. The orbital HK model exhibits dynamical mixing across the Mott gap, namely dynamical spectral weight transfer (DSWT), a key non-trivial feature of the Hubbard model. But unlike Hubbard, exact solvability is not sacrificed.
Based on: https://arxiv.org/abs/2401.08746
