Quantum magnetism in moiré Wigner molecules

Moiré superlattices in transition metal dichalcogenides (TMDs) have provided a platform to engineer quantum solids composed of artificial atoms sitting on moiré sites. In particular, we focus on the case of three electrons per site. Due to the strong electronic interaction the moiré atom's three electrons form a trimer called a Wigner molecule. This leads to an emerging pattern of localized charges forming a breathing kagome lattice. Besides the charge, the molecules carry spin and orbital angular momentum (OAM) degrees of freedom which paves the opportunity to study the interplay between the two. We aim to uncover the interactions of the localized spin and orbital degrees of freedom of these molecules. By integrating out the fluctuating charge degrees of freedom, we arrive at a Hamiltonian that only includes the interactions between the spins and the OAM which is quite distinct from the conventional Heisenberg model. Finally, we study the magnetic ground state using two complementary numerical techniques - exact diagonalization and DMRG.