Revisiting the Gross-Neveu-Heisenberg transition with accelerated projective quantum Monte Carlo

The Gross-Neveu-Heisenberg transition has attracted significant attention due to its relevance to the mass generation mechanism of Dirac fermions. The simplest lattice realization is the Hubbard model on the honeycomb lattice, but previous simulations exhibit large finite-size effects near the critical point. We propose a state-of-the-art algorithm for local updates in projective quantum Monte Carlo on CPU that simultaneously optimizes cache usage and computational scalability. Benchmarked against both fast update and former delayed update algorithms, it demonstrates clear advantages in computational efficiency. We apply it to revisit the semimetal-insulator transition in the Hubbard model on honeycomb lattices with sizes up to $72\times 72\times 2$. By analyzing the finite-size scaling of the correlation ratio, squared staggered magnetization, and Green's function, we extract critical exponents including $\nu$, $\eta_\phi$, and $\eta_\psi$, and examine their convergence behavior with increasing system size.