# Transition from a Dirac spin liquid to an antiferromagnet: Monopoles in a QED3-Gross-Neveu theory

## TL;DR

This paper investigates the quantum phase transition from a Dirac spin liquid to an antiferromagnet, focusing on monopole operators, critical exponents, and the monopole hierarchy at the critical point using conformal field theory techniques.

## Contribution

It introduces a detailed analysis of monopole operator scaling dimensions and degeneracy lifting at the QCP in a QED3-Gross-Neveu framework, including a test of duality with a bosonic CP^1 theory.

## Key findings

- Monopole degeneracy is lifted, leading to a hierarchy at the QCP.
- The lowest monopole scaling dimension is approximately 0.39N_f at leading order.
- The study confirms a duality between the Dirac spin liquid transition and a bosonic CP^1 theory.

## Abstract

We study the quantum phase transition from a Dirac spin liquid to an antiferromagnet driven by condensing monopoles with spin quantum numbers. We describe the transition in field theory by tuning a fermion interaction to condense a spin-Hall mass, which in turn allows the appropriate monopole operators to proliferate and confine the fermions. We compute various critical exponents at the quantum critical point (QCP), including the scaling dimensions of monopole operators by using the state-operator correspondence of conformal field theory. We find that the degeneracy of monopoles in QED3 is lifted and yields a non-trivial monopole hierarchy at the QCP. In particular, the lowest monopole dimension is found to be smaller than that of QED3 using a large $N_f$ expansion where $2N_f$ is the number of fermion flavors. For the minimal magnetic charge, this dimension is $0.39N_f$ at leading order. We also study the QCP between Dirac and chiral spin liquids, which allows us to test a conjectured duality to a bosonic CP$^1$ theory. Finally, we discuss the implications of our results for quantum magnets on the Kagome lattice.