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

Abstract

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 CP${}^{N\ensuremath{-}1}$ 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 CP${}^{N\ensuremath{-}1}$ 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 N\'eel 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.