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

Abstract

In this paper, we study quantum Sp(N) antiferromagnetic (AF) Heisenberg models in two dimensions (2D) by using the Schwinger-boson representation and the pathintegral 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 "Néel 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.

Three-dimensional antiferromagneticCPN−1models

“…Because of the presence of the cubic term, on the basis of meanfield arguments, one expects the system to undergo a first-order transition for any N > 2, unless the Hamiltonian parameters are tuned so that w = 0 in the effective model. This prediction is, however, contradicted by recent numerical studies [2,8,10,11], which find evidence of continuous transitions in models that are expected to be in the same universality class as that of the 3D CP 2 model. In particular, a numerical study of 3D loop models [8] provided the estimate ν = 0.536 (13) for the correlation-length critical exponent.…”

“…We confirm the RG predictions by comparing the FSS behavior of the O(8) vector and ACP 2 models, obtained by MC simulations of both lattice models. We note that the critical behavior, characterized by the O(8) critical exponents ν = 0.85(2) and η = 0.0276(5), definitely differs from that of ferromagnetic CP 2 models, for which recent studies [2,8,10,11] have provided numerical evidence of continuous transitions with critical exponents ν = 0.536 (13) and η = 0.23 (2).…”

Phase transitions in three-dimensional loop models and theCPn−1sigma model

“…Large loop fugacity favours the disordered phase of loop models, which occupies a growing portion of the phase diagram with increasing n. More detailed features vary with the choice of lattice: for one (termed the K-lattice below) we find a first-order transition at n ≥ 4 between ordered and disordered phases; another (the three-dimensional L-lattice) supports only disordered phases at n ≥ 5. First order transitions have also been reported 23,24 from Monte Carlo simulations of other lattice discretisations of the CP n−1 model at n = 4, and from an analytical treatment of the large-n limit.…”

Two-dimensional multicomponent Abelian-Higgs lattice models

“…Models of complex scalar matter fields with abelian and nonabelian gauge symmetries effectively emerge in several interesting systems, such as superconductors and superfluids, quantum Hall states, quantum SU(N ) antiferromagnets, unconventional quantum phase transitions, etc., see, e.g., Refs. [1][2][3][4][5][6][7][8][9][10][11][12] and references therein. Among the paradigmatic models considered, an important role is played by the multicomponent lattice Abelian-Higgs (AH) model or lattice scalar electrodynamics, which is a lattice U(1) gauge theory coupled with an N -component complex scalar field, characterized by a global SU(N ) symmetry.…”