Correlated phases in moiré triangular lattice Hubbard model: a DMRG study

Moiré transition metal dichalcogenide (TMD) systems provide an unprecedented experimental platform for exploring triangular lattice Hubbard physics and the interplay between geometric frustration and electronic correlations. However, although the conventional triangular lattice Hubbard model has been extensively studied in both theory and numerics, its moiré counterpart, particularly the effects of displacement field, remains largely unexplored. In this work, we employ large scale density matrix renormalization group (DMRG) simulations to study a minimal moiré Hubbard model on triangular lattice with nearest-neighbor hopping and spin-dependent flux. At half filling, our results reveal metallic, chiral spin liquid, and magnetic ordered phases. Increasing displacement field gradually suppresses the chiral spin liquid regime, driving the metal-insulator and spin-ordering transition lines to intersect and subsequently influence the magnetic phases; the magnetic phases also show evidence of a commensurate-incommensurate transition. Upon doping away from half filling, the phase diagram becomes even richer, reflecting the intricate interplay between charge and spin degrees of freedom. Our findings shed light on how displacement field control and electronic interactions govern correlated phases in moiré TMD systems, providing valuable guidance toward the experimental realization of a quantum spin liquid.