Effective field theory for Sp(N) antiferromagnets and their phase structure

In this paper, we study quantum Sp(N) antiferromagnetic (AF) Heisenberg models by using the Schwinger-boson representation and the path-integral methods. We consider both the two-dimensional (2D) system at vanishing temperature and the 3D system at finite temperature (T). An effective field theory, which is an extension of the CPN-1 model in 3D, is derived and its phase structure is studied with the 1/N expansion. We also introduce a lattice gauge theoretical model of CPN-1 bosons, which is a counterpart of the effective field theory in the continuum, and study its phase structure by means of Monte Carlo simulations. For SU(N) AF magnets on the 2D square lattice, which is a specific case of the Sp(N) model, we introduce a spatial anisotropy in the exchange couplings and show that a phase transition from the ordered Neel state to the paramagnetic phase takes place as the anisotropy is increased. On the other hand for the 3D Sp(N) system at finite T, we clarify the global phase structure. 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 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. This is another example of the symmetry-enhancement phenomenon at low energies. As it is expected that the Sp(4) AF magnets are realized by cold spin-3/2 fermions in an optical lattice, the above results might be verified by experiments in the near future.