Moire systems provide a rich platform for studies of strong correlation physics. Recent experiments on hetero-bilayer transition metal dichalcogenide (TMD) Moire systems are exciting in that they manifest a relatively simple model system of an extend
ed Hubbard model on a triangular lattice. Inspired by the prospect of the hetero-TMD Moire systems potential as a solid-state-based quantum simulator, we explore the extended Hubbard model on the triangular lattice using the density matrix renormalization group (DMRG). Specifically, we explore the two-dimensional phase space of the kinetic energy relative to the interaction strength $t/U$ and the further-range interaction strength $V_1/U$. We find competition between Fermi fluid, chiral spin liquid, spin density wave, and charge density wave. In particular, our finding of the optimal further-range interaction for the chiral correlation presents a tantalizing possibility.
