  We design a novel formalism of determinant quantum Monte Carlo method for the
half-filled Hubbard model with on-site Hubbard interaction $U$ and nearest
neighbor density-density interaction $V$ on the square lattice. The formalism
is free of sign problem for $|U|\ge 4|V|$, and is achieved by introducing
discrete auxiliary fields on the nearest-neighbor bonds alone. Based on this
formalism, we study the ground state phase diagram of the model systematically
using the projector algorithm. Within the sign-problem free parameter space
$|U|\ge 4|V|$, we obtain antiferromagnetism for $U\ge 4|V|>0$, charge density
wave for $U<-4V$ and $V>0$, s-wave superconductivity for $U<0$ and small
negative $V$, and phase separation for $U<0$ and a larger negative $V$. We also
obtain the single particle gap and spin excitation spectra, and by comparison
to mean field results, as well as available literatures, we discuss the
possible phase boundary beyond the sign-problem free region. The unbiased
numerically exact results can be taken as benchmarks in future studies.
Finally, we discuss possible extension for longer-range interactions in the
model.

Strongly Correlated Electrons;Superconductivity