The Generalized Ideal Band Condition for FCIs

Fractional Chern insulators (FCIs) are a strongly correlated phase of topological matter which exhibits a fractionally quantized Hall effect in the absence of an external magnetic field. Recently, so-called ideal band conditions constraining the single-particle quantum geometry of the partially-filled band have been proposed as markers of the stability of a many-body FCI ground state. The first and most well-known ideal band condition is the trace condition. This talk discusses a generalization of the trace condition which allows the choice of holomorphic coordinate to act as a variational parameter, and its relevance to anisotropic systems.