Anomalous dimensions of monopole operators at the transitions between Dirac and topological spin liquids

The quantum phase transitions between a Dirac spin liquid and two types of topological spin liquids (chiral and Z_{2} spin liquids) are considered. The transitions are described by conformal field theories (CFTs) consisting of quantum electrodynamics in 2+1 dimensions with 2N flavors of two-component massless Dirac fermions and a four-fermion interaction. For the transition to a chiral spin liquid, it is the Gross-Neveu interaction (QED_{3}-GN), while for the transition to the Z_{2} spin liquid it is a superconducting pairing term (QED_{3}-Z_{2}GN). We study monopole operators at these quantum critical points using a large-N expansion to subleading order in 1/N. The scaling dimension of a QED_{3}-GN monopole with minimal charge is found to be very close to the scaling dimensions of other operators predicted to be equal by a conjectured duality between QED_{3}-GN with 2N=2 flavors and the bosonic CP^{1} model. By studying the large-charge asymptotics of the scaling dimensions in both QED_{3}-GN and QED_{3}-Z_{2}GN, we verify that the coefficient of the constant term precisely matches the universal prediction for CFTs with a global U(1) symmetry.