Ferromagnetic Semimetal and Charge-Density Wave Phases of Interacting Electrons in a Honeycomb Moiré Potential

The exploration of quantum phases in moiré systems has drawn intense experimental and theoretical efforts. The realization of honeycomb symmetry has been a recent focus. The combination of strong interaction and honeycomb symmetry can lead to exotic electronic states such as fractional Chern insulator, unconventional superconductor, and quantum spin liquid. Accurate computations in such systems, with reliable treatment of long-ranged Coulomb interaction and approaching large system sizes to extract thermodynamic phases, are mostly missing. We study the two-dimensional electron gas on a honeycomb moiré lattice at quarter filling, using the fixed-phase diffusion Monte Carlo method. The ground state phases of this important model are determined in the parameter regime relevant to current experiments. With increasing moiré potential, the system transitions from a paramagnetic metal to an itinerant ferromagnetic semimetal then a charge-density-wave insulator.