Fermionic spinon theory of square lattice spin liquids near the Néel state

Quantum fluctuations of the Néel state of the square lattice antiferromagnet are usually described by a CP¹ theory of bosonic spinons coupled to a U(1) gauge field with a global SU(2) spin rotation symmetry. Such a theory also has a confining phase with valence bond solid (VBS) order and deconfined phases with Z₂ topological order. We present dual theories of these phases starting from a mean-field theory of fermionic spinons with a π-flux in each plaquette. Fluctuations about this π-flux state are described by 2+1 dimensional quantum chromodynamics (QCD₃) with a SU(2) gauge group and N_f= 2 flavors of massless Dirac fermions. It has recently been argued by Wang et al. (arXiv:1703.02426) that this theory describes the Néel-VBS phase transition. We introduce adjoint Higgs fields in QCD₃, and obtain fermionic descriptions of both the VBS phase and the topologically ordered phases obtained earlier using the bosonic theory. The global phase diagram of these phases contains multi-critical points, and our results imply new boson-fermion dualities.