Deconfined Quantum Criticality and Conformal Phase Transition in Two-Dimensional Antiferromagnets

TL;DR

This paper presents a new field-theoretic approach to deconfined quantum criticality in 2D antiferromagnets, revealing a conformal phase transition that leads to a genuine quantum critical point with universal properties.

Contribution

It introduces an epsilon-expansion framework for deconfined quantum critical points, showing the existence of a conformal phase transition in regimes previously thought to be weakly first-order.

Findings

Identification of a conformal phase transition in the weak first-order regime.

Universal jump in spin stiffness at the critical point.

Genuine deconfined quantum critical point emerging from the transition.

Abstract

Deconfined quantum criticality of two-dimensional $SU(2)$ quantum antiferromagnets featuring a transition from an antiferromagnetically ordered ground state to a so-called valence-bond solid state, is governed by a non-compact CP$^1$ model with a Maxwell term in 2+1 spacetime dimensions. We introduce a new perspective on deconfined quantum criticality within a field-theoretic framework based on an expansion in powers of $\epsilon=4-d$ for fixed number $N$ of complex matter fields. We show that in the allegedly weak first-order transition regime, a so-called conformal phase transition leads to a genuine deconfined quantum critical point. In such a transition, the gap vanishes when the critical point is approached from above and diverges when it is approached from below. We also find that the spin stiffness has a universal jump at the critical point.