Fermionic theory for quantum antiferromagnets with spin S > 1/2

Abstract

The fermion representation for S = 1/2 spins is generalized to spins with arbitrary magnitudes. The symmetry properties of the representation is analyzed where we find that the particle-hole symmetry in the spinon Hilbert space of S =1/2 fermion representation is absent for S > 1/2. As a result, different path integral representations and mean field theories can be formulated for spin models. In particular, we construct a Lagrangian with restored particle-hole symmetry, and apply the corresponding mean field theory to one dimensional (1D) S = 1 and S = 3/2 antiferromagnetic Heisenberg models, with results that agree with Haldane's conjecture. For a S = 1 open chain, we show that Majorana fermion edge states exist in our mean field theory. The generalization to spins with arbitrary magnitude S is discussed. Our approach can be applied to higher dimensional spin systems. As an example, we study the geometrically frustrated S = 1 AFM on triangular lattice. Two spin liquids with different pairing symmetries are discussed: the gapped px + ipy-wave spin liquid and the gapless f-wave spin liquid. We compare our mean field result with the experiment on NiGa2S4, which remains disordered at low temperature and was proposed to be in a spin liquid state. Our fermionic mean field theory provide a framework to study S > 1/2 spin liquids with fermionic spinon excitations.

16 pages, 4 figures

References in corpus (19)

• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Z_2 Gauge Theory of Electron Fractionalization in Strongly Correlated Systems
• U(1) Gauge Theory of the Hubbard Model : Spin Liquid States and Possible Application to k-(BEDT-TTF)_2 Cu_2 (CN)_3
• On the stability of U(1) spin liquids in two dimensions
• The quadrupolar phases of the S=1 bilinear-biquadratic Heisenberg model on the triangular lattice
• Spin Nematic Phase in S=1 Triangular Antiferromagnets
• Implementation of Spin Hamiltonians in Optical Lattices
• An SU(2) Formulation of the t-J model: Application to Underdoped Cuprates
• Dimer Order with Striped Correlations in the J_1-J_2 Heisenberg Model
• Dimer state of spin-1 Bosons in an optical lattice
• Possible ferro-spin nematic order in NiGa2S4
• Quadrupolar correlations and spin freezing in S = 1 triangular lattice antiferromagnets
• Vortex-induced topological transition of the bilinear-biquadratic Heisenberg antiferromagnet on the triangular lattice
• The SU(3) bosons and the spin nematic state on the spin-1 bilinear-biquadratic triangular lattice
• Topologically distinct classes of valence bond solid states with their parent Hamiltonians
• Possibility of S=1 spin liquids with fermionic spinons on triangular lattices
• Swapping and permutation operators as entanglement witnesses for quantum Heisenberg spin-$s$ systems
• Modelling the Berezinskii-Kosterlitz-Thouless Transition in the NiGa_2S_4
• Supersymmetric Mean-Field Theory of t-J Model

Cited by in corpus (32)

• Quantum Spin Liquid States
• Classification and Properties of Symmetry Enriched Topological Phases: A Chern-Simons approach with applications to Z2 spin liquids
• Projective symmetry group classification of chiral spin liquids
• Numerical treatment of spin systems with unrestricted spin length $S$: A functional renormalization group study
• Paired chiral spin liquid with a Fermi surface in S=1 model on the triangular lattice
• Exotic S=1 spin liquid state with fermionic excitations on triangular lattice
• Evidence for a spinon Fermi surface in the triangular S=1 quantum spin liquid Ba${}_3$NiSb${}_2$O${}_9$
• Projected BCS states and spin Hamiltonians for the SO(n)_1 Wess-Zumino-Witten model
• Pseudo-fermion functional renormalization group for spin models
• Topology and Criticality in Resonating Affleck-Kennedy-Lieb-Tasaki loop Spin Liquid States
• $U(1)\times U(1)$ Symmetry Protected Topological Order in Gutzwiller Wave Functions
• Projective studies of spin nematics in a quantum frustrated ferromagnet
• Finite and Infinite Matrix Product States for Gutzwiller Projected Mean-Field Wavefunctions
• Efficient tensor network representation for Gutzwiller projected states of paired fermions
• Classification of spin liquids on the square lattice with strong spin-orbit coupling
• Gutzwiller Projected wavefunctions in the fermonic theory of S=1 spin chains
• A non-abelian spin-liquid in a spin-1 quantum magnet
• Gapless chiral spin liquid from coupled chains on the kagome lattice
• Non-Abelian Chiral Spin Liquid on the Kagome Lattice
• Spin quantum Hall effects in a spin-1 topological paramagnet
• Hexagon-singlet solid ansatz for the spin-1 kagome antiferromagnet
• Bilinear Majorana representations for spin operators with spin magnitudes $S>1/2$
• Quantum spin liquids on the diamond lattice
• Resonating valence bond realization of spin-1 non-Abelian chiral spin liquid on the torus
• Ground States of Heisenberg Spin Clusters from Projected Hartree-Fock Theory
• Multinode quantum spin liquids in extended Kitaev honeycomb models: the view from variational Monte Carlo
• Topological edge states in spin 1 bilinear-biquadratic model
• Projective symmetry group classification of $Z_3$ parafermion spin liquids on a honeycomb lattice
• Overscreened Kondo fixed point in S=1 spin liquid
• Abelian and non-Abelian quantum spin liquids in a three-component Bose gas on optical Kagome lattices
• Representation Theory for Massless Quasiparticles in Bogoliubov-de Gennes Systems
• Symmetry-protected topological order identified via Gutzwiller-guided density-matrix-renormalization-group: $\mathrm{SO}(n)$ spin chains