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We investigate the ground state phase diagram of an extended Hubbard modelwith $\pi$-flux hopping term at half-filling on a square lattice, with unbiasedlarge-scale auxiliary-field quantum Monte Carlo simulations. As a function ofinteraction strength, there emerges an intermediate phase which realizes twointeraction-driven quantum critical points, with the first between the Diracsemimetal and an insulating phase of weak valence bond solid (VBS) order, andthe second separating the VBS order and an antiferromagnetic insulating phase.These intriguing quantum critical points are respectively bestowed withGross-Neveu and deconfined quantum criticalities, and the critical exponents$\eta_\text{VBS}=0.6(1)$ and $\eta_\text{AF}=0.58(3)$ at deconfined quantumcritical point satisfy the CFT Bootstrap bound. We also investigate thedynamical properties of the spin excitation and find the spin gap open near thefirst transition and close at the second. The relevance of our findings inrealizing deconfined quantum criticality in fermion systems and the implicationto lattice models with further extended interactions such as those in quantumMoir\'e systems, are discussed.

Dirac fermions with plaquette interactions. I. SU(2) phase diagram with Gross-Neveu and deconfined quantum criticalities