Mott Transition in the Square-Lattice SU(4) Fermionic Hubbard Model with a π-Flux Gauge Field

Inspired by recent ultracold atom experiments in both the synthetic gauge field and the SU(2N) symmetry, by employing the large-scale projector quantum Monte Carlo simulations, we investigate the ground state properties of the square-lattice SU(4) fermionic Hubbard model with a π-flux gauge field. In the noninteracting limit, the ground state is the gapless Dirac semimetal. With the increase of repulsive interaction, we show that, in the presence of a π-flux gauge field per plaquette, a Mott transition occurs from the semimetal to the valence bond solid phase, accompanied by the breaking of Z₄ discrete symmetry. The phase transition point and the critical exponent have also been estimated by the finite size scaling of numerical data. Interestingly, in the strong coupling limit we have analyzed the role of ring exchange terms for the order formation of the ground state by perturbation theory.