  We employ the cluster slave-spin method to investigate systematically the
ground state properties of the Hubbard model on a square lattice with doping
$\delta$ and coupling strength $U$ being its parameters. In addition to a
crossover reflected in the behavior of the antiferromagnetic gap
$\Delta_{\text{AFM}}$, this property can also be observed in the energetics of
the cluster slave-spin Hamiltonian -- the antiferromagnetism at small $U$ is
due to the potential energy gain while that in the strong coupling limit is
driven by the kinetic energy gain, which is consistent with the results from
the cluster dynamical mean-field theory calculation and the quantum Monte Carlo
simulation. We find the interaction $U_{c}$ for the crossover in the AFM state,
separating the weak- and strong- coupling regimes, almost remains unchanged
upon doping, and it is smaller than the critical coupling strength
$U_{\text{Mott}}$ for the first-order metal-insulator Mott transition in the
half-filled paramagnetic state. At half-filling, a relationship between the
staggered magnetization $M$ and $\Delta_{\text{AFM}}$ is established in the
small $U$ limit to nullify the Hartree-Fock theory, and a first-order Mott
transition in the paramagnetic state is substantiated, which is characterized
by discontinuities and hystereses at $U_{\text{Mott}}=10t$. Finally, an overall
phase diagram in the $U$-$\delta$ plane is presented, which is composed of four
regimes: the antiferromagnetic insulator, the antiferromagnetic metal with the
compressibility $\kappa>0$ or $\kappa<0$, and the paramagnetic metal, as well
as three phase transitions: (i) From the antiferromagnetic metal to the
paramagnetic metal, (ii) between the antiferromagnetic metal phases with
positive and negative $\kappa$, and (iii) separating the antiferromagnetic
insulating phase from the antiferromagnetic metal phase.
