Mott Insulating States of Anisotropic SU(4) Dirac Fermions

We employ large-scale projector quantum Monte Carlo simulations to study the ground-state properties of the SU(4) Hubbard model on a square lattice with a staggered flux configuration. By varying the on-site repulsion and the flux, our simulations demonstrate phase transions between the Dirac semimetal, antiferromagnetic (AFM) and valence-bond-solid (VBS) phases. We find a continuous AFM-VBS phase transition. The direct second-order transition between different symmetry-breaking phases suggests deconfined critical points which form the boundary between the AFM and VBS phases. Near the deconfined critical points, we show that the AFM and VBS Binder ratios have the same critical exponents. As Hubbard U increases, the VBS order drops to zero, while the AFM moment has a finite value in the Heisenberg limit. It infers that the system with any flux eventually enters the AFM phases with increasing Hubbard U. By analysis of the gap opening mechanism, it is shown that both the columnar VBS ordering and the plaquette VBS ordering emerge in the VBS phase, and thus the phase diagram features two tricritical points where the semimetal, AFM and VBS phases meet.