Critical torus spectrum of the Gross-Neveu-Yukawa field theory*

We compute the low-energy critical torus spectrum of the Gross-Neveu-Yukawa universality class, which features N=4 component Dirac spinors that spontaneously break a Z₂ chiral symmetry, in D=(2+1) dimensions. A possible lattice realization of such Dirac fermions is provided by the interacting t-V model of spinless fermions on the honeycomb lattice. We use a combination of Exact Diagonalization and Quantum Monte Carlo simulations to compute the energy spectrum on finite-size clusters with periodic boundaries, and perform an extrapolation to the thermodynamic limit. We show that the interaction between the spinor field and the scalar order-parameter field strongly influences the torus spectrum at the critical point, and propose the critical spectrum as a universal fingerprint of the critical Gross-Neveu-Yukawa field theory. Moreover, we estimate the renormalization of the Fermi velocity in the Dirac phase from the interaction induced corrections to the energy spectrum, and extrapolate the observed linear renormalization up to the critical point. Finally, we contrast the Fermi velocity renormalization in the spinless t-V model with the situation in the spinful Hubbard model.