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

TL;DR

This paper demonstrates that adding a topological Chern-Simons term to the easy-plane CP^1 model of 2D antiferromagnets transforms the expected first-order transition into a continuous one with quantized critical exponents, revealing a new deconfined criticality.

Contribution

It introduces a topological Chern-Simons term into the easy-plane CP^1 model, showing it induces a second-order transition and a duality to massless Dirac fermions, advancing understanding of deconfined quantum critical points.

Findings

Chern-Simons term changes transition order from first to second

Transition exhibits quantized critical exponents

Partition function maps to massless Dirac fermions

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.