Moiré superlattices in van der Waals bilayers can dramatically alter material properties. I will present theoretical proposals of using moiré bilayers as a quantum simulation platform to realize model Hamiltonians. In semiconducting transition metal dichalcogenide (TMD) heterobilayers, isolated flat moiré bands can be used to simulate Fermi-Hubbard model on a triangular lattice, in which parameters such as bandwidth, interaction strength, and band filling are widely tunable. Excitons in twisted TMD bilayers also experience moiré potential, which can be used to modulate optical spectrum and to simulate Bose-Hubbard model.
