Orbital XY models in moiré superlattices

Moiré superlattices provide a new platform to engineer various many-body problems. In this work, we consider arrays of quantum dots (QD) realized on semiconductor moiré superlattices with a deep moiré potential. We diagonalize single QD with multiple electrons, and find degenerate ground states serving as local degrees of freedom (qudits) in the superlattice. With a deep moiré potential, the hopping and exchange interaction between nearby QDs become irrelevant, and the direct Coulomb interaction of the density–density type dominates. Therefore, nearby QDs must arrange the spatial densities to optimize the Coulomb energy. When the local Hilbert space has a two-fold orbital degeneracy, we find that a square superlattice realizes an anisotropic XY model, while a triangular superlattice realizes a generalized XY model with geometric frustration.