We investigate ground state properties of spin-1 bosonic system trapped in
optical lattice with extended standard basis operator (SBO) method. For both
ferromagnetic (U2​0) systems, we
analytically figure out the symmetry properties in Mott-insulator and
superfluid phases, which would provide a deeper insight into the MI-SF phase
transition process. Then by applying self-consistent approach to the method, we
include the effect of quantum and thermal fluctuations and derive the MI-SF
transition phase diagram, which is in quantitative agreement with recent
Monte-Carlo simulation at zero temperature, and at finite temperature, we find
the underestimation of finite-temperature-effect in the mean-field
approximation method. If we further consider the spin excitations in the
insulating states of spin-1 system in external field, distinct spin phases are
expected. Therefore, in the Mott lobes with n=1 and n=2 atoms per site, we
give analytical and numerical boundaries of the singlet, nematic, partially
magnetic and ferromagnetic phases in the magnetic phase diagrams.Comment: 14 pages, 6 figure