Monte Carlo Study of Finite-Temperature Critical Dynamics of Interacting Dirac Fermions at the Gross-Neveu-Heisenberg Transition

We investigate the finite-temperature critical dynamics of interacting Dirac fermions at the antiferromagnetic quantum critical point of the half-filled Hubbard model on the honeycomb lattice, which belongs to the Gross-Neveu-Heisenberg universality class. Using large-scale determinant quantum Monte Carlo (DQMC) simulations free of sign problem, we access the quantum critical regime and compute dynamical observables directly relevant to transport and spectroscopy. In particular, we extract the fermionic self-energy near the Dirac points, and the current-current correlator across a wide temperature window. Our results provide a nonperturbative benchmark for field-theoretical predictions of Gross-Neveu-Yukawa-type theories and furnish controlled lattice evidence for universal finite-temperature dynamical scaling in interacting Dirac systems.