Monopole operators are studied at certain quantum critical points between a Dirac spin liquid and topological quantum spin liquids (QSLs): chiral and Z2 QSLs. These quantum phase transitions are described by conformal field theories (CFTs): quantum electrodynamics in 2+1 dimensions with 2N flavors of two-component massless Dirac fermions and a four-fermion interaction term. For the transition to a chiral spin liquid, it is the Gross-Neveu interaction (QED3-GN), while for the transition to the Z2 QSL it is a superconducting pairing term (QED3-Z2GN). Using the state-operator correspondence, we obtain monopole scaling dimensions to sub-leading order in 1/N . For monopoles with a minimal topological charge q = 1/2, the scaling dimension is 2N × 0.26510 at leading-order, with the quantum correction being 0.118911(7) for the chiral spin liquid, and 0.102846(9) for the Z2 case. Although these two anomalous dimensions are nearly equal, the underlying quantum fluctuations possess distinct origins. The analogous result in QED3 is also obtained and we find a sub-leading contribution of −0.038138(5), which is slightly different from the value −0.0383 first obtained in the literature. The scaling dimension of a QED3-GN monopole with minimal charge is very close to the scaling dimensions of other operators predicted to be equal by a conjectured duality between QED3-GN with 2N = 2 flavors and the CP 1 model. Additionally, non-minimally charged monopoles with equal charges on both sides of the duality have similar scaling dimensions. By studying the large-q asymptotics of the scaling dimensions in QED3, QED3-GN, and QED3-Z2GN we verify that the constant O(q 0 ) coefficient precisely matches the universal prediction for CFTs with a global U(1) symmetry. CONTENTS A. Large N non-compact quantum phase transition B. Scalar-gauge kernel C. Gauge invariance Verifications D. Green's function 1. Eigenvalues of determinant operator 2. Green's function E. Eigenkernels 1. First basis 2. Second basis 3. Kernel coefficients for general q F. Results for the q = 1/2 computations G. Remainder coefficients H. Only zero modes contribution in the kernels Generalization I. Fitting procedure for anomalous dimensions J. Monopole scaling dimensions for 1/2 ≤ q ≤ 13 References

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 SU(2) × SU(N f ) symmetric QCP.

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