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.
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Notes
- 1.
In vector notation using spherical coordinates on Euclidean spacetime
, it would be written as \(A^q_\mu = q(1-\cos \theta )/(r \sin \theta ) \delta _\mu ^{\phi }\). - 2.
Divergences in the gap equation are treated with a Zeta regularization.
- 3.
Divergences in the scaling dimension and the related gap equation are treated with a zeta function regularization. It is important to keep the same regularization scheme that was used to determine the critical effective action in the non-compact theory (7).
- 4.
Note that contrary to other transitions described in Sect. 1, here the symmetric mass generates a Chern–Simons term which prevents monopole proliferation.
, it would be written as References
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We thank Tarun Grover, Joseph Maciejko, David Poland, Zi Yang Meng and Chong Wang for the interesting discussions and useful observations on our work during the symposium. We also thank Jaume Gomis and Sergueï Tchoumakov for useful discussions. É.D. was funded by an Alexander Graham Bell CGS from NSERC. M.B.P. was funded by a Discovery Grant from NSERC. W.W.-K. was funded by a Discovery Grant from NSERC, a Canada Research Chair, a grant from the Fondation Courtois, and a “Établissement de nouveaux chercheurs et de nouvelles chercheuses universitaires” grant from FRQNT.
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Dupuis, É., Paranjape, M.B., Witczak-Krempa, W. (2021). Monopole Operators and Their Symmetries in QED3-Gross–Neveu Models. In: Paranjape, M.B., MacKenzie, R., Thomova, Z., Winternitz, P., Witczak-Krempa, W. (eds) Quantum Theory and Symmetries. CRM Series in Mathematical Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-55777-5_31
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