  In this paper, we study quantum Sp(N) antiferromagnetic (AF) Heisenberg
models in two dimensions (2D) by using the Schwinger-boson representation and
the path-integral methods. An effective field theory, which is an extension of
CP^{N-1} model in (2+1)D, is derived and its phase structure is studied by the
1/N-expansion. We introduce a spatial anisotropy in the exchange couplings and
show that the effective coupling constant in the CP^{N-1} model is an
increasing function of the anisotropy. For the SU(N) AF Heisenberg model, which
is a specific case of the Sp(N) model, we found that phase transition from the
ordered "N\'eel state" to paramagnetic phase takes place as the anisotropy is
increased. In the vicinity of the SU(N) symmetric point, this phase structure
is retained. However as a parameter that controls explicit breaking of the
SU(N) symmetry is increased, a new phase, which is similar to the spiral-spin
phase with a nematic order in frustrated SU(2) spin systems, appears. It is
shown that at that phase transition point, a local SU(2) gauge symmetry with
composite SU(2) gauge field appears in the low-energy sector. It is another
example of symmetry-enhancement phenomenon at low energies. We also introduce a
lattice gauge-theoretical model, which is a counterpart of the effective field
theory, and study its phase structure by means of the Monte-Carlo simulations.
