Unconventional Metallic States in a Two-orbital Square-Lattice Moiré Hubbard Model

We investigate the many-body physics of a p_x,p_y-orbital Hubbard model with intra- and inter-orbital interactions. This model is directly motivated by the low-energy excited bands of newly proposed twisted bilayer Γ-valley square lattice systems. Starting from quarter filling, we perform a strong-coupling expansion to derive an effective Hamiltonian. We find that this model naturally includes significant four-site ring-exchange terms, which are known to frustrate conventional superfluid and charge-ordered states. The presence of these terms provides a microscopic route to exploring exotic, compressible quantum phases beyond the Landau-Ginzburg paradigm. We use variational Monte Carlo (VMC) to map the ground state phase diagram, focusing on the competition between conventional orders and potential unconventional metallic states. We analyze the behavior of relevant correlation functions and momentum-space structures to characterize the emergent phases, providing a guide for realizing non-Fermi-liquid physics in an engineered 2D material.