Effective XY Model in Morié Superlattice.*

Moiré superlattices provide a platform to simulate various many-body problems. In this work, we consider arrays of quantum dots (QDs) realized on moiré superlattice with large moiré lattice constant. We do exact-diagonalization for single QD with multiple electrons, and find degenerate ground states that serve as local degree of freedom of the superlattice. According to scaling analysis, exchange and hopping between nearby QDs are irrelevant at the large lattice constant limit, and the dominating effect is the direct Coulomb repulsion. Particular configurations of the local ground states where electron clouds between nearby QDs have as little as possible overlap can save the Coulomb energy. When the local Hilbert space is two-dimensional, we find the superlattice realizes an effective anisotropic XY model.