Exact Results in Flat Band Hubbard Models

Flat bands, like those in the kagome lattice or twisted bilayer graphene, are a natural setting for studying strongly coupled physics, since the interaction strength is the only energy scale in the problem. They can exhibit unconventional behavior in the multi-orbital case: mean-field theory of flat band attractive Hubbard models shows the possibility of superconductivity even though the Fermi velocity of the bands is strictly zero. However, it is not necessary to resort to this approximation. We demonstrate that the groundstates and low-energy excitations of a large class of attractive Hubbard models are exactly solvable, offering a rare, microscopic view of their physics. The solution reveals the importance of quantum geometry in escaping (some of) BCS phenomenology. I will discuss these results, ongoing research, and open questions about these models.

Zoom recording link