Monopole Operators and Their
Symmetries in QED 3 -Gross–Neveu
Models
Éric Dupuis, M. B. Paranjape, and William Witczak-Krempa
Abstract Monopole operators are topological disorder operators in 2 + 1 dimensional compact gauge field theories appearing notably in quantum magnets with
fractionalized excitations. For example, their proliferation in a spin-1/2 kagome
Heisenberg antiferromagnet triggers a quantum phase transition from a Dirac spin
liquid phase to an antiferromagnet. The quantum critical point (QCP) for this transition is described by a conformal field theory: Compact quantum electrodynamics
(QED 3 ) with a fermionic self-interaction, a type of QED 3 -Gross–Neveu model. We
obtain the scaling dimensions of monopole operators at the QCP using a stateoperator correspondence and a large-N f expansion, where 2N f is the number
of fermion flavors. We characterize the hierarchy of monopole operators at this
SU(2) × SU(N f ) symmetric QCP.
Keywords Topological disorder operators · Gauge theories and dualities ·
Quantum phase transition · Quantum spin liquids · Conformal field theory
1 Confinement of a Dirac Spin Liquid
An abelian gauge theory consists of the Maxwell term for the gauge field a μ and
potentially some matter coupled through a U(1) charge
L =
1
2e 2
μνρ ∂ ν a ρ
2 + Matter charged under U(1).
(1)
É. Dupuis ()
Département de physique, Université de Montréal, Montréal, QC, Canada
e-mail: eric.dupuis.1@umontreal.ca
M. B. Paranjape · W. Witczak-Krempa
Département de physique, Université de Montréal, Montréal, QC, Canada
Centre de Recherches Mathématiques, Université de Montréal, Montréal, QC, Canada
e-mail: paranj@lps.umontreal.ca; w.witczak-krempa@umontreal.ca
© Springer Nature Switzerland AG 2021
M. B. Paranjape et al. (eds.), Quantum Theory and Symmetries, CRM Series in
Mathematical Physics, https://doi.org/10.1007/978-3-030-55777-5_31
327
Symmetries in QED 3 -Gross–Neveu
Models
Éric Dupuis, M. B. Paranjape, and William Witczak-Krempa
Abstract Monopole operators are topological disorder operators in 2 + 1 dimensional compact gauge field theories appearing notably in quantum magnets with
fractionalized excitations. For example, their proliferation in a spin-1/2 kagome
Heisenberg antiferromagnet triggers a quantum phase transition from a Dirac spin
liquid phase to an antiferromagnet. The quantum critical point (QCP) for this transition is described by a conformal field theory: Compact quantum electrodynamics
(QED 3 ) with a fermionic self-interaction, a type of QED 3 -Gross–Neveu model. We
obtain the scaling dimensions of monopole operators at the QCP using a stateoperator correspondence and a large-N f expansion, where 2N f is the number
of fermion flavors. We characterize the hierarchy of monopole operators at this
SU(2) × SU(N f ) symmetric QCP.
Keywords Topological disorder operators · Gauge theories and dualities ·
Quantum phase transition · Quantum spin liquids · Conformal field theory
1 Confinement of a Dirac Spin Liquid
An abelian gauge theory consists of the Maxwell term for the gauge field a μ and
potentially some matter coupled through a U(1) charge
L =
1
2e 2
μνρ ∂ ν a ρ
2 + Matter charged under U(1).
(1)
É. Dupuis ()
Département de physique, Université de Montréal, Montréal, QC, Canada
e-mail: eric.dupuis.1@umontreal.ca
M. B. Paranjape · W. Witczak-Krempa
Département de physique, Université de Montréal, Montréal, QC, Canada
Centre de Recherches Mathématiques, Université de Montréal, Montréal, QC, Canada
e-mail: paranj@lps.umontreal.ca; w.witczak-krempa@umontreal.ca
© Springer Nature Switzerland AG 2021
M. B. Paranjape et al. (eds.), Quantum Theory and Symmetries, CRM Series in
Mathematical Physics, https://doi.org/10.1007/978-3-030-55777-5_31
327