Frozen deconfined quantum criticality

TL;DR

This paper demonstrates that easy-plane quantum antiferromagnets exhibit a deconfined quantum critical point (DQCP), resolving previous contradictions by establishing a second-order phase transition through lattice duality and renormalization group analysis.

Contribution

The study provides the first exact lattice duality and RG analysis confirming the existence of a DQCP in easy-plane CP1 antiferromagnets, linking bosonic and fermionic theories at criticality.

Findings

Confirmation of a second-order phase transition at the DQCP

Duality between bosonic and fermionic theories at criticality

Identification of a 'frozen' classical regime leading to criticality

Abstract

There is a number of contradictory findings with regard to whether the theory describing easy-plane quantum antiferromagnets undergoes a second-order phase transition. The traditional Landau-Ginzburg-Wilson approach suggests a first-order phase transition, as there are two different competing order parameters. On the other hand, it is known that the theory has the property of self-duality which has been connected to the existence of a deconfined quantum critical point (DQCP). The latter regime suggests that order parameters are not the elementary building blocks of the theory, but rather consist of fractionalized particles that are confined in both phases of the transition and only appear - deconfine - at the critical point. Nevertheless, many numerical Monte Carlo simulations disagree with the claim of a DQCP in the system, indicating instead a first-order phase transition. Here we establish from exact lattice duality transformations and renormalization group analysis that the easy-plane CP1 antiferromagnet does feature a DQCP. We uncover the criticality starting from a regime analogous to the zero temperature limit of a certain classical statistical mechanics system which we therefore dub "frozen". At criticality our bosonic theory is dual to a fermionic one with two massless Dirac fermions, which thus undergoes a second-order phase transition as well.