  We study the phase diagram of repulsively interacting spin-1 bosons in
optical lattices at unit filling, showing that an externally induced quadratic
Zeeman effect may lead to a rich physics characterized by various phases and
phase transitions. We find that the main properties of the system may be
described by an effective field model, which provides the precise location of
the phase boundaries for any dimension, being in excellent agreement with our
numerical calculations for one-dimensional systems. Our work provides a
quantitative guide for the experimental analysis of various types of
field-induced quantum phase transitions in spin-1 lattice bosons. These
transitions, which are precluded in spin-1/2 systems, may be realized using an
externally modified quadratic Zeeman coupling, similar to recent experiments
with spinor condensates in the continuum.
