Solvable Models of non-Fermi liquids with non-trivial bandstructure

Motivated by recent experimental studies in correlated materials with non-Fermi liquid behavior and extra local degrees of freedom, we construct minimal solvable models of a non-Fermi liquid with non-trivial band structure such as flat bands or band-inversions. These models rely on higher-dimensional extensions of the Sachdev-Ye-Kitaev (SYK) model. Typical lattice generalizations of the SYK model cross over to a Fermi liquid at low-temperatures. Notable exceptions consist of models with divergent density of Bloch states. We investigate the role that increased density of states arising naturally from band-touching points and flat-bands can have on this nFL-FL crossover. We also examine the effect these considerations have on various symmetry-broken resulting phases. Analytic and numerical techniques are used to explore the interplay of various forms of SYK-type interactions with novel band structures, and their resulting transport properties.