Symplectic N and time reversal in frustrated magnetism

Abstract

Identifying the time reversal symmetry of spins as a symplectic symmetry, we develop a large N approximation for quantum magnetism that embraces both antiferromagnetism and ferromagnetism. In SU(N), N>2, not all spins invert under time reversal, so we have introduced a new large N treatment which builds interactions exclusively out of the symplectic subgroup [SP(N)] of time reversing spins, a more stringent condition than the symplectic symmetry of previous SP(N) large N treatments. As a result, we obtain a mean field theory that incorporates the energy cost of frustrated bonds. When applied to the frustrated square lattice, the ferromagnetic bonds restore the frustration dependence of the critical spin in the Neel phase, and recover the correct frustration dependence of the finite temperature Ising transition.

added references

References in corpus (15)

• Magnetic Order versus superconductivity in the Iron-based layered La(O1-xFx)FeAs systems
• Strong Correlations and Magnetic Frustration in the High Tc Iron Pnictides
• Spin-Liquid State in the S = 1/2 Hyperkagome Antiferromagnet Na4Ir3O8
• Origin of the ~150 K Anomaly in LaOFeAs; Competing Antiferromagnetic Superexchange Interactions, Frustration, and Structural Phase Transition
• Ising and Spin orders in Iron-based Superconductors
• On the stability of U(1) spin liquids in two dimensions
• Dimensional reduction at a quantum critical point
• Topological spin liquid on the hyper-kagome lattice of Na_4Ir_3O_8
• Heavy electrons and the symplectic symmetry of spin
• Supplementary material to Heavy electrons and the symplectic symmetry of spin
• Classical antiferromagnet on a hyperkagome lattice
• Ising transition in the two-dimensional quantum $J_1-J_2$ Heisenberg model
• Flux expulsion and greedy bosons: frustrated magnets at large N
• Quantum phase transitions and dimensional reduction in antiferromagnets with inter-layer frustration
• Semiclassical ordering in the large-N pyrochlore antiferromagnet

Cited by in corpus (26)

• Time-reversal-symmetry-breaking chiral spin liquids: a projective symmetry group approach of bosonic mean-field theories
• Exotic disordered phases in the quantum $J_1-J_2$ model on the honeycomb lattice
• Quantum magnetism of ultra-cold fermion systems with the symplectic symmetry
• Qudit quantum computation on matrix product states with global symmetry
• Low temperature properties of the triangular-lattice antiferromagnet: a bosonic spinon theory
• Projective symmetry group classification of chiral ${\mathbb{Z}}_2$ spin liquids on the pyrochlore lattice: application to the spin-$1/2$ XXZ Heisenberg model
• Schwinger boson theory of ordered magnets
• Electromagnetic signatures of chiral quantum spin liquid
• Simulating a two-dimensional frustrated spin system with fermionic resonating-valence-bond states
• One dimensionalization in the spin-1 Heisenberg model on the anisotropic triangular lattice
• Effective field theory for Sp(N) antiferromagnets and its phase structure
• Evidence of a spin liquid phase in the frustrated honeycomb lattice
• Schwinger Boson mean field theory of kagome Heisenberg antiferromagnet with Dzyaloshinskii-Moriya interaction
• ${\mathbb{Z}}_2$ metallic spin liquid on a frustrated Kondo lattice
• Schwinger boson theory of the J1,J2=J3 kagome antiferromagnet
• Spin current Kondo effect in frustrated Kondo systems
• The Symplectic Fermi Liquid and its realization in cold atomic systems
• The symplectic-N t-J model and s${}_{\pm }$ superconductors
• Chiral bosonic quantum spin liquid in the integer-spin Heisenberg-Kitaev model
• Field-driven transition from quantum spin liquid to magnetic order in triangular-lattice antiferromagnets
• Quantum order by disorder in Frustrated Spin Nanotubes
• Random matrix model for antiferromagnetism and superconductivity on a two-dimensional lattice
• Dynamic-RKKY induced time-reversal symmetry breaking and chiral spin liquids
• Relevance of Anisotropy in the Kondo Effect: Lessons From the Symplectic Case
• Schwinger boson theory for $S=1$ Kitaev quantum spin liquids
• Dynamical spin correlations in kagome antiferromagnets: comparison of Abrikosov fermion and Schwinger boson approaches beyond mean field