Hubbard model on the honeycomb lattice with an indefinite long-range interaction

Several studies have emphasized the impact of long-range Coulomb interactions in lattice fermions, yet conventional auxiliary field quantum Monte Carlo (QMC) methods face limitations due to their reliance on positive-definite interaction matrices. We address this by decomposing the interaction matrix into positive- and negative-definite components, allowing for QMC calculations with manageable sign properties. This technique enables effective simulations on large lattices. Applying it to a honeycomb lattice with an indefinite interaction matrix, we identify a semimetal to the charge density wave phase transition within the Gross-Neveu criticality class. Notably, the phase transition boundary aligns with regions where the average sign sharply decreases, providing evidence to the increasingly compelling research on the relationship between phase transitions and the sign problem.