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

Models with long-range interactions - known as Hatsugai -Kohmoto (HK) models - have emerged as a promising tool to study superconductivity and topology in strongly interacting systems. These models display the hallmarks of Mott insulation and non-Fermi liquid behaviour. Previous models, however, tended to suffer from extensive ground state degeneracies and an instability towards a symmetry-broken magnetic state. In this talk, we remedy both issues by constructing a more general class of HK model. Our generalized models have non- or finitely-degenerate ground states, and can easily be extended to systems which do not conserve spin. They thus realize Mott insulating, spin liquid ground states that preserve all space group and time-reversal symmetries. This opens the way to use these models as a platform to study the topology of strongly interacting systems. We begin to explore this direction by showing that generalized HK models can violate crystal-symmetry enriched Lieb-Schultz Mattis theorems for short-range entangled systems.