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

TL;DR

This paper extends fermionic spin representations to arbitrary spin magnitudes, analyzes their symmetry properties, and applies mean field theories to various models, including 1D chains and frustrated lattices, revealing new insights into spin liquids and edge states.

Contribution

It introduces a generalized fermionic representation for spins with S > 1/2, analyzes its symmetry properties, and develops mean field theories applicable to higher-dimensional and frustrated spin systems.

Findings

Mean field theory agrees with Haldane's conjecture for S=1 and S=3/2 chains.

Existence of Majorana edge states in S=1 open chains.

Identification of two distinct spin liquid states on triangular lattices.

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.