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 ${\mathrm{QED}}_{3}$ is lifted and yields a nontrivial monopole hierarchy at the QCP. In particular, the lowest monopole dimension is found to be smaller than that of ${\mathrm{QED}}_{3}$ using a large- ${N}_{f}$ expansion, where $2{N}_{f}$ is the number of fermion flavors. For the minimal magnetic charge, this dimension is $0.39{N}_{f}$ 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 ${\mathrm{CP}}^{1}$ theory. Finally, we discuss the implications of our results for quantum magnets on the kagome lattice.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 ${\mathrm{QED}}_{3}$ is lifted and yields a nontrivial monopole hierarchy at the QCP. In particular, the lowest monopole dimension is found to be smaller than that of ${\mathrm{QED}}_{3}$ using a large-${N}_{f}$ expansion, where $2{N}_{f}$ is the number of fermion flavors. For the minimal magnetic charge, this dimension is $0.39{N}_{f}$ 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 ${\mathrm{CP}}^{1}$ theory. Finally, we discuss the implications of our results for quantum magnets on the kagome lattice.

arXiv:1905.02750Physical review. B./Physical review. BSep 27, 201933 citations

{\mathrm{QED}}_{3}

is lifted and yields a nontrivial monopole hierarchy at the QCP. In particular, the lowest monopole dimension is found to be smaller than that of

{\mathrm{QED}}_{3}

using a large-

{N}_{f}

expansion, where

2{N}_{f}

is the number of fermion flavors. For the minimal magnetic charge, this dimension is

0.39{N}_{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

{\mathrm{CP}}^{1}

theory. Finally, we discuss the implications of our results for quantum magnets on the kagome lattice.