  Based on standard field-theoretic considerations, we develop an effective
action approach for investigating quantum phase transitions in lattice Bose
systems at arbitrary temperature. We begin by adding to the Hamiltonian of
interest a symmetry breaking source term. Using time-dependent perturbation
theory, we then expand the grand-canonical free energy as a double power series
in both the tunneling and the source term. From here, an order parameter field
is introduced in the standard way, and the underlying effective action is
derived via a Legendre transformation. Determining the Ginzburg-Landau
expansion to first order in the tunneling term, expressions for the Mott
insulator-superfluid phase boundary, condensate density, average particle
number, and compressibility are derived and analyzed in detail. Additionally,
excitation spectra in the ordered phase are found by considering both
longitudinal and transverse variations of the order parameter. Finally, these
results are applied to the concrete case of the Bose-Hubbard Hamiltonian on a
three dimensional cubic lattice, and compared with the corresponding results
from mean-field theory. Although both approaches yield the same Mott insulator
- superfluid phase boundary to first order in the tunneling, the predictions of
our effective action theory turn out to be superior to the mean-field results
deeper into the superfluid phase.
