Haldane pseudopotentials and correlations in twisted TMD homobilayer FQAHE states

The fractional quantum anomalous Hall effect (FQAHE) observed in TMD homobilayers is thought to be related to flat Chern bands and to effective magnetic fields produced by real-space Berry phases associated with the layer-dependent terms in the Hamiltonian. We will report on a generalization to the TMD homobilayer case of the Haldane pseudopotential concept that Is useful in the analysis of ordinary quantum Hall effects. We define Haldane pseudopotentials in terms of eigenvalues of the two-particle interaction Hamiltonian projected to the flat Chern band, and parameterize correlations in terms of the occupation probabilities of two-particle states in the many-electron ground state. We show that the the properties of these two quantities are similar to the analogous quantities in ordinary Landau levels when the flat Chern band has approximately ideal quantum geometry, and discuss generalizations of the Laughlin and Jain many-body state constructions to the flat Chern band case.