Fermionic Spinon Theory of Square Lattice Spin Liquids near the Néel State
Abstract
Quantum fluctuations of the Néel state of the square lattice antiferromagnet are usually described by a CP^{1} 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 spinsinglet charge2 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 meanfield theory of fermionic spinons moving in π flux in each square lattice plaquette. Fluctuations about this π 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)., 10.1103/PhysRevX.7.031051] that this QCD_{3} theory describes the NéelVBS 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 CP^{1} 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 bosonfermion dualities between critical gauge theories of these points.
 Publication:

Physical Review X
 Pub Date:
 January 2018
 DOI:
 10.1103/PhysRevX.8.011012
 arXiv:
 arXiv:1708.04626
 Bibcode:
 2018PhRvX...8a1012T
 Keywords:

 Condensed Matter  Strongly Correlated Electrons;
 High Energy Physics  Theory
 EPrint:
 Version 2: 32 pages, 3 figures, 12 tables