Mott insulating states of the anisotropic SU(4) Dirac fermions

We employ the large-scale quantum Monte-Carlo simulations to investigate the Mott-insulating states of the half-filled SU(4) Hubbard model on the square lattice with a staggered-flux pattern. The noninteracting band structure that evolves from a nested Fermi surface at zero flux to isotropic Dirac cones at $\pi$ flux, exhibits anisotropic Dirac cones as the flux varies in between. Our simulations show transitions between the three phases of Dirac semimetal, antiferromagnet and valence-bond solid. A direct continuous transition between the antiferromagnetic phase and the valence-bond-solid phase is realized via varying the flux in the Mott regime. The simulated critical exponents remarkably agree with those of SU(4) $J$-$Q$ model. Inside the valence-bond-solid phase induced by the flux, the plaquette valence-bond state with vanishing single-particle gap is identified. At strong coupling, the valence-bond-solid phase disappears and the Mott-insulating state is always accompanied by antiferromagnetic ordering, regardless of the magnitude of the flux.