1/4 is the new 1/2: Emergent Mottness at Quarter filling in the Haldane and KM/BHZ models

While the recent advances in topology have led to a classification scheme for electronic bands described by the standard theory of metals, a similar scheme has not emerged for strongly correlated systems such as Mott insulators in which a partially filled band carries no current. This talk will address this deficiency by including interactions into the three dominant models for topological states, the Haldane and KM/BHZ models. We show that all of these models possess a quarter-filled state that is an insulator once the interactions exceed the bandwidth. We obtain this result by solving analytically the HK model in which the interactions are local in momentum space and then numerically by quantum Monte Carlo simulations on the corresponding Hubbard model. The consilience between HK and Hubbard stems from a fixed point that underlies all Mott systems. Recent experiments on the anomalous quantum Hall effect in transition metal dichalcogenides are discussed in this context.