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