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

Journal Article · Fri May 01 04:00:00 EDT 2009 · Physical Review. B, Condensed Matter and Materials Physics

DOI:https://doi.org/10.1103/PHYSREVB.79.184429· OSTI ID:21287014

Hermele, Michael ^[1]

---

1. Department of Physics, University of Colorado, Boulder, Colorado 80309 (United States)

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 nonperturbative 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.

• OSTI ID: 21287014
• Journal Information: Physical Review. B, Condensed Matter and Materials Physics, Journal Name: Physical Review. B, Condensed Matter and Materials Physics Journal Issue: 18 Vol. 79; ISSN 1098-0121
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOSON EXPANSION
BOSONS
CRITICALITY
DUALITY
FERMIONS
GAUGE INVARIANCE
INFORMATION
LATTICE FIELD THEORY
LEAD
MAGNETS
SPACE-TIME
SU-2 GROUPS
SUPERSYMMETRY
TWO-DIMENSIONAL CALCULATIONS
U-1 GROUPS
VECTORS
VORTICES
WAVELENGTHS