Mott transition in the $π$-flux SU($4$) Hubbard model on a square lattice

Abstract

We employ the projector quantum Monte Carlo simulations to study the ground-state properties of the square-lattice SU(4) Hubbard model with a $π$ flux per plaquette. In the weak coupling regime, its ground state is in the gapless Dirac semi-metal phase. With increasing repulsive interaction, we show that, a Mott transition occurs from the semimetal to the valence bond solid, accompanied by the $Z_4$ discrete symmetry breaking. Our simulations demonstrate the existence of a second-order phase transition, which confirms the Ginzburg-Landau analysis. The phase transition point and the critical exponent $η$ are also estimated. To account for the effect of a $π$ flux on the ordering in the strong coupling regime, we analytically derive by the perturbation theory the ring-exchange term which describes the leading-order difference between the $π$-flux and zero-flux SU(4) Hubbard models.