Critical behavior of the QED3-Gross-Neveu model: Duality and deconfined criticality

2017/08/31 by Lukas Janssen, Yin-Chen He · 1 citation
Physics and Astronomy · #Advanced Condensed Matter Physics #Critical exponent #Critical phenomena #Gauge theory #Mathematical physics #Phase transition #Physics #Physics of Superconductivity and Magnetism #Quantum critical point #Quantum mechanics #Quantum phase transition #Scalar (mathematics) #Topological Materials and Phenomena #cond-mat.stat-mech #cond-mat.str-el #hep-th

paper · pdf · doi:10.1103/physrevb.96.205113

published as Phys. Rev. B 96, 205113 (2017) · 12 pages, 7 figures, 1 table; v2: loop diagrams added, additional comments and references, published version

openalex created_date 2017/08/17 · openalex publication_date 2017/11/08 · arxiv created 2017/11/09 · arxiv updated 2017/11/10 · openalex updated_date 2026/08/05

Abstract

We study the critical properties of the QED₃-Gross-Neveu model with 2N flavors of two-component Dirac fermions coupled to a massless scalar field and a U(1) gauge field. For N=1, this theory has recently been suggested to be dual to the SU(2) noncompact CP¹ model that describes the deconfined phase transition between the N'eel antiferromagnet and the valence bond solid on the square lattice. For N=2, the theory has been proposed as an effective description of a deconfined critical point between chiral and Dirac spin liquid phases, and may potentially be realizable in spin-1/2 systems on the kagome lattice. We demonstrate the existence of a stable quantum critical point in the QED₃-Gross-Neveu model for all values of N. This quantum critical point is shown to escape the notorious fixed-point annihilation mechanism that renders plain QED₃ (without scalar-field coupling) unstable at low values of N. The theory exhibits an upper critical space-time dimension of four, enabling us to access the critical behavior in a controlled expansion in the small parameter \ensuremathε=4\ensuremath-D. We compute the scalar-field anomalous dimension \ensuremathη_\ensuremathφ, the correlation-length exponent \ensuremathν, as well as the scaling dimension of the flavor-symmetry-breaking bilinear \ensuremathψ\ensuremathσ^z\ensuremathψ at the critical point, and compare our leading-order estimates with predictions of the conjectured duality.

Citations

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Cited by

• Note on Wess-Zumino-Witten models and quasiuniversality in 2+1 dimensions