M is for Monte Carlo: a sign-free Quantum Monte Carlo study of M-point moiré materials

A new, fundamentally different moiré platform was recently proposed based on twisting monolayer materials with triangular lattices and low-energy states around the M-point of the Brillouin zone [1]. These M-point moiré materials realize multi-orbital Hubbard models with emergent quasi-one-dimensionality within each valley. We show that this structure renders them sign-problem-free at all fillings within Quantum Monte Carlo and investigate their interacting physics. Over a broad and realistic range of angles and interaction strengths, we find correlated insulators at integer fillings whose nature and robustness depend strongly on the twist angle, as well as Wigner–Mott insulators at certain commensurate fillings. The main numerical features are understood analytically using bosonization and strong-coupling approaches.

[1] D. Călugăru et al., Nature 643, 376 (2025).