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

arXiv comment22+7 pages, 9+4 figures, 7 tables. v2: Additional discussion about the transition to a chiral spin liquid allowing us to test a conjectured duality to a bosonic CP1 theory

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• Quantum phase transitions in Dirac fermion systems
• Confinement transition in the QED${}_3$-Gross-Neveu-XY universality class
• Dynamics of Compact Quantum Electrodynamics at Large Fermion Flavor
• Evidence of Two-Spinon Bound States in the Magnetic Spectrum of Ba${}_3$CoSb${}_2$O${}_9$
• Anomalous dimensions of monopole operators at the transitions between Dirac and topological spin liquids
• Critical properties of the Néel/algebraic-spin-liquid transition
• Critical properties of the valence-bond-solid transition in lattice quantum electrodynamics
• Superfluids, vortices and spinning charged operators in 4d CFT
• Monopole Josephson Effects in a Dirac Spin Liquid
• Random-mass disorder in the critical Gross-Neveu-Yukawa models
• Solving quantum rotor model with different Monte Carlo techniques
• Frustrated Kondo impurity triangle: A simple model of deconfinement
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• Evidence for 3d bosonization from monopole operators
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