Effective field theory for Sp(N) antiferromagnets and its 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 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 "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.

30 pages, 15 figures

References in corpus (21)

• "Deconfined" quantum critical points
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Quantum magnetism and criticality
• Exact SO(5) Symmetry in spin 3/2 fermionic system
• SU(4) Theory for Spin Systems with Orbital Degeneracy
• Hidden symmetry and quantum phases in spin-3/2 cold atomic systems
• Néel and Spin-Peierls ground states of two-dimensional SU(N) quantum antiferromagnets
• Heavy electrons and the symplectic symmetry of spin
• Supplementary material to Heavy electrons and the symplectic symmetry of spin
• The SU(N) Heisenberg model on the square lattice: a continuous-N quantum Monte Carlo study
• Large-N solutions of the Heisenberg and Hubbard-Heisenberg models on the anisotropic triangular lattice: application to Cs${}_2$CuCl${}_4$ and to the layered organic superconductors $\kappa$-(BEDT-TTF)${}_2$X
• Comprehensive quantum Monte Carlo study of the quantum critical points in planar dimerized/quadrumerized Heisenberg models
• Symplectic N and time reversal in frustrated magnetism
• Valence bond solid states with symplectic symmetry
• Néel-Dimer Transition in Antiferromagnetic Heisenberg Model and Deconfinement of Spinons at the Critical Point
• Quantum Phase Transitions beyond the Landau's Paradigm in Sp(4) Spin System
• Four-dimensional CP${}^1+$ U(1) lattice gauge theory for 3D antiferromagnets: Phase structure, gauge bosons and spin liquid
• Antiferromagnetic, metal-insulator, and superconducting phase transitions in underdoped cuprates: Slave-fermion t-J model in the hopping expansion
• Phase structure of $Z_2$ gauge theories for frustrated antiferromagnets in two dimensions
• Low Energy Effective Field Theories of Sp(4) Spin systems
• Phase Structure of Anisotropic Antiferromagnetic Heisenberg Model on Layered Triangular Lattice: Spiral State and Deconfined Spin Liquid

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