Monopole hierarchy in transitions out of a Dirac spin liquid

TL;DR

This paper investigates the hierarchy and properties of monopole operators at quantum critical points in Dirac spin liquids, revealing how their scaling dimensions depend on magnetic spin and symmetry group organization.

Contribution

It introduces a detailed analysis of monopole operator hierarchy at QCPs in Dirac spin liquids using large-N expansion and symmetry group organization.

Findings

Monopoles with maximal spin have the smallest scaling dimension.

Monopoles with zero magnetic spin have the largest scaling dimension.

Monopole organization in SU(2) x SU(N) symmetry multiplets is characterized.

Abstract

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.