Hyperdeterminants and composite fermion states in fractional Chern insulators

Writing down wavefunctions for fractional quantum Hall states was a milestone of condensed matter physics. Here, the authors achieve this goal for the newly discovered fractional quantum anomalous Hall effect (FQAHE), by developing a projective construction for composite fermion (CF) states, and revealing hyperdeterminants as a general structure for electronic wavefunctions. This construction is able to capture the microscopics, and is used to compute many observables in FCI states that are hard to do via traditional methods, including CF dispersion and the magnetoroton spectrum.