Monopole Operators and Their Symmetries in QED3-Gross–Neveu Models

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 (QED3) with a fermionic self-interaction, a type of QED3-Gross–Neveu model. We obtain the scaling dimensions of monopole operators at the QCP using a state-operator 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 $$ \operatorname {\mathrm {SU}}(2) \times \operatorname {\mathrm {SU}}(N_f)$$ symmetric QCP.