Optical experiments utilize excitons (electron-hole bound states) in moir ́e transition metal dichalcogenide bilayers as a quantum simulator of the Bose-Hubbard model. Nevertheless, we show that these excitations possess nonbosonic commutation relations due to their composite nature, limiting the size of phase space for them to occupy. Such an effect manifests at weak electron-hole correlation, and restricts the number of excitons to be less than 4 per site and valley for three different bilayers. In addition, we develop a nonlinear bosonic representation for these excitons with general statistics and utilize it to show that the exciton Hamiltonian is of the Bose-Hubbard category with an occupancy constraint. Our work provides guidelines for future research on many-body physics with moir ́e excitons.

Pizza and drinks will be served after the seminar in ATL 2117.