Fermionic Spinon Theory of Square Lattice Spin Liquids near the Neel State

Quantum fluctuations of the Neel state of the square lattice antiferromagnet are usually described by a CP1 theory of bosonic spinons coupled to a U(1) gauge field, and with a global SU(2) spin rotation symmetry. Such a theory also has a confining phase with valence bond solid (VBS) order, and upon including spin-singlet charge-2 Higgs fields, deconfined phases with Z(2) topological order possibly intertwined with discrete broken global symmetries. We present dual theories of the same phases starting from a mean-field theory of fermionic spinons moving in pi flux in each square lattice plaquette. Fluctuations about this pi-flux state are described by (2 + 1)-dimensional quantum chromodynamics (QCD(3)) with a SU(2) gauge group and N-f = 2 flavors of massless Dirac fermions. It has recently been argued by Wang et al. [Deconfined Quantum Critical Points: Symmetries and Dualities, Phys. Rev. X 7, 031051 (2017).] that this QCD(3) theory describes the Neel-VBS quantum phase transition. We introduce adjoint Higgs fields in QCD(3) and obtain fermionic dual descriptions of the phases with Z(2) topological order obtained earlier using the bosonic CP1 theory. We also present a fermionic spinon derivation of the monopole Berry phases in the U(1) gauge theory of the VBS state. The global phase diagram of these phases contains multicritical points, and our results imply new boson-fermion dualities between critical gauge theories of these points.