Correlation effects in M-point moiré materials at half-filling: A Determinant Quantum Monte Carlo Approach

M-point moiré materials are a newly proposed platform based on twisted monolayers whose low-energy electronic states are concentrated near the M points of the Brillouin zone [1]. These systems realize multi-orbital Hubbard models with strong hopping anisotropy due to their approximate symmetries. We show that these realistic models allow for a sign-problem-free determinant quantum Monte Carlo (DQMC) analysis at half filling of the lowest conduction band. The valley degrees of freedom in this model lead to a rich phase diagram which we map out, using DQMC, identifying regimes with antiferromagnetism, charge density waves, and strongly renormalized Fermi-metal behavior. We further place various M-point moiré candidates—corresponding to different materials, twist angles and interaction strengths—within this phase diagram, providing a unified framework for understanding their correlated phases.

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