Non-abelian descendant of abelian duality in a two-dimensional frustrated quantum magnet

Abstract

Several recent works on quantum criticality beyond the Landau-Ginzburg-Wilson paradigm have led to a number of field theories, potentially important for certain two-dimensional magnetic insulating systems, where criticality is not very well understood. This situation highlights the need for non-perturbative information about criticality in two spatial dimensions (three space-time dimensions), which is a longstanding challenge. As a step toward addressing these issues, we present evidence that the O(4) vector model is dual to a theory of Dirac fermions coupled to both SU(2) and U(1) gauge fields. Both field theories arise as low-energy, long-wavelength descriptions of a frustrated XY model on the triangular lattice. Abelian boson-vortex duality of the lattice model, together with the emergence of larger non-abelian symmetry at low energies, leads to this rare example of duality in two spatial dimensions involving non-abelian global symmetry and fermions, but without supersymmetry. The duality can also be viewed as a bosonization of the Dirac fermion gauge theory.

arXiv comment12 pages + 3 appendices. 3 figures. Minor change, typos corrected

References in corpus (33)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
• Critical Phenomena and Renormalization-Group Theory
• "Deconfined" quantum critical points
• Bosonization and Strongly Correlated Systems
• Quantum Orders and Symmetric Spin Liquids
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Mirror Symmetry in Three Dimensional Gauge Theories
• Projected wavefunction study of Spin-1/2 Heisenberg model on the Kagome lattice
• On the stability of U(1) spin liquids in two dimensions
• Universality of phase transitions of frustrated antiferromagnets
• Properties of an algebraic spin liquid on the kagome lattice
• On Mirror Symmetry in Three Dimensional Abelian Gauge Theories
• Topological Disorder Operators in Three-Dimensional Conformal Field Theory
• Algebraic spin liquid as the mother of many competing orders
• Algebraic Fermi liquid from phase fluctuations: "topological" fermions, vortex "berryons" and QED3 theory of cuprate superconductors
• Competing orders, non-linear sigma models, and topological terms in quantum magnets
• Nonperturbative renormalization group approach to frustrated magnets
• Electron spectral function and algebraic spin liquid for the normal state of underdoped high $T_c$ superconductors
• Theta-terms in nonlinear sigma-models
• Spin correlations in the algebraic spin liquid - implications for high Tc superconductors
• Algebraic charge liquids
• Critical behavior of O(2)xO(N) symmetric models
• Algebraic vortex liquid theory of a quantum antiferromagnet on the kagome lattice
• Monopoles in CP(N-1) model via the state-operator correspondence
• Criticality in quantum triangular antiferromagnets via fermionized vortices
• Algebraic vortex liquid in spin-1/2 triangular antiferromagnets: Scenario for Cs_2CuCl_4
• Relativity Restored: Dirac Anisotropy in QED${}_3$
• The Renormalization Group Studies on Four Fermion Interaction Instabilities on Algebraic Spin Liquids
• Theory of the algebraic vortex liquid in an anisotropic spin-1/2 triangular antiferromagnet
• Monopole Quantum Numbers in the Staggered Flux Spin Liquid
• Erratum: algebraic spin liquid as the mother of many competing orders
• A square lattice algebraic spin liquid with SO(5) symmetry

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• Fractionalized gapless quantum vortex liquids