  We examine the zero and finite temperature phase diagrams of soft-core bosons
of the extended Bose-Hubbard model on a square optical lattice. To study
various quantum phases and their transitions we employ single-site and cluster
Gutzwiller mean-field theory. We have observed that the Mott insulator phase
vanishes above a critical value of nearest-neighbour interaction and the
supersolid phase occupies a larger region in the phase diagram. We show that
the presence of artificial gauge field enlarges the domain of supersolid phase.
The finite temperature destroys the crystalline structure of the supersolid
phase and thereby favours normal fluid to superfluid phase transition. The
presence of an envelope harmonic potential demonstrates coexistence of
different phases and at $z~k_{B}T\geqslant V$, thermal energy comparable and
higher to the long-range interaction energy, the supersolidity of the system is
destroyed.
