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Recently, models with long-range interactions -- known as Hatsugai-Kohmoto(HK) models -- have emerged as a promising tool to study the emergence ofsuperconductivity and topology in strongly correlated systems. Two obstacles,however, have made it difficult to understand the applicability of thesemodels, especially to topological features: they have thermodynamically largeground state degeneracies, and they tacitly assume spin conservation. We showthat neither are essential to HK models and that both can be avoided byintroducing interactions between tight-binding states in the orbital basis,rather than between energy eigenstates. To solve these "orbital" models, weintroduce a general technique for solving HK models and show that previousmodels appear as special cases. We illustrate our method by exactly solvinggraphene and the Kane-Mele model with HK interactions. Both realize Mottinsulating phases with finite magnetic susceptibility; the graphene model has afourfold degenerate ground state while the Kane-Mele model has a nondegenerateground state in the presence of interactions. Our technique then allows us tostudy the effect of strong interactions on symmetry-enforced degeneracy inspin-orbit coupled double-Dirac semimetals. We show that adding HK interactionsto a double Dirac semi-metal leads to a Mott insulating, spin liquid phase. Wethen use a Schrieffer-Wolff transformation to express the low-energyHamiltonian in terms of the spin degrees of freedom, making the spin-chargeseparation explicit. Finally, we enumerate a broader class ofsymmetry-preserving HK interactions and show how they can violate insulatingfilling constraints derived from space group symmetries. This suggests that newapproaches are needed to study topological order in the presence of long-rangeinteractions of the HK type.

Ground state stability, symmetry, and degeneracy in Mott insulators with long range interactions