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

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 (LGW) 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 CP¹ model. A delicate issue however is that numerics indicate the easy-plane CP¹ antiferromagnet to exhibit a first-order transition. We will explore the intricate critical behavior of this model through the particle-vortex duality and demonstrate an overlooked critical regime in the dual model. Furthermore, we will show that an additional topological Chern-Simons term in the action changes this picture completely in several ways. We will find that the topological easy-plane antiferromagnet undergoes a second-order transition with quantized critical exponents. Moreover, a particle-vortex duality naturally maps the partition function of the Chern-Simons easy-plane antiferromagnet into one of massless Dirac fermions.