  Quantum spin liquids host novel emergent excitations, such as monopoles of an
emergent gauge field. Here, we study the hierarchy of monopole operators that
emerges at quantum critical points (QCPs) between a two-dimensional Dirac spin
liquid and various ordered phases. This is described by a confinement
transition of quantum electrodynamics in two spatial dimensions (QED3
Gross-Neveu theories). Focusing on a spin ordering transition, we get the
scaling dimension of monopoles at leading order in a large-N expansion, where
2N is the number of Dirac fermions, as a function of the monopole's total
magnetic spin. Monopoles with a maximal spin have the smallest scaling
dimension while monopoles with a vanishing magnetic spin have the largest one,
the same as in pure QED3. The organization of monopoles in multiplets of the
QCP's symmetry group SU(2) x SU(N) is shown for general N.

Strongly Correlated Electrons;High Energy Physics - Theory