Hyperdeterminant wavefunctions 

Fractional quantum anomalous Hall states have been experimentally discovered recently. Understanding these phases of matter microscopically remains a theoretical challenge. I will show that all the composite fermion states in these systems can be compactly represented as the hyperdeterminant wavefunctions – a direct generalization of the Slater determinant wavefunctions to tensors. These hyperdeterminants are generalizations of the conventional fermionic parton constructions previously applied in the context of fractional quantum Hall states and quantum spin liquids. Practical simulation methods for hyperdeterminants will be discussed.