Anomalous Dimensions of Monopole Operators at the Transitions

Monopole operators are studied in a large family of quantum critical points between Dirac spin liquids 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 transitions to Z2 QSLs, it is a superconducting pairing term with general spin and valley structure (generalized QED3-Z2GN). Using the state-operator correspondence, we obtain monopole scaling dimensions to subleading 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 simplest Z2 case (the expression is also given for a general pairing term). 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 subleading 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 CP1 model. Additionally, nonminimally 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(q0) coefficient precisely matches the universal nonperturbative prediction for CFTs with a global U(1) symmetry. Finally, we identify numerous open questions regarding the fate of monopoles and their hierarchies at transitions to spin liquids and ordered phases.

Automated summary

This study investigates monopole operators in various quantum critical points, deriving scaling dimensions using the state-operator correspondence. It examines scenarios in quantum electrodynamics and transitions to topological quantum spin liquids.