Deconfined criticality and bosonization duality in easy-plane Chern-Simons two-dimensional antiferromagnets

Abstract

Two-dimensional quantum systems with competing orders can feature a deconfined quantum critical point, yielding a continuous phase transition that is incompatible with the Landau-Ginzburg-Wilson scenario, predicting instead a first-order phase transition. This is caused by the LGW order parameter breaking up into new elementary excitations at the critical point. Canonical candidates for deconfined quantum criticality are quantum antiferromagnets with competing magnetic orders, captured by the easy-plane CP${}^1$ model. A delicate issue however is that numerics indicates the easy-plane CP${}^1$ antiferromagnet to exhibit a first-order transition. Here we show that an additional topological Chern-Simons term in the action changes this picture completely in several ways. We find that the topological easy-plane antiferromagnet undergoes a second-order transition with quantized critical exponents. Further, a particle-vortex duality naturally maps the partition function of the Chern-Simons easy-plane antiferromagnet into one of massless Dirac fermions.

v2: published version includes Supplemental Material containing details of calculations and 4 figures; references added

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• Bosonization duality in 2+1 dimensions and critical current correlation functions in Chern-Simons $U(1)\times U(1)$ Abelian Higgs model
• Topological Phase Transition in a Quasi Two Dimensional Coulomb Gas
• Critical Behavior and Duality in Dimensionally Reduced Planar Chern-Simons Superconductors
• Topology-driven deconfined quantum criticality in magnetic bilayers
• Superselection Rules, Bosonization Duality in 1+1 Dimensions and Momentum-Space Entanglement