Deconfined quantum critical points: symmetries and dualities

TL;DR

This paper explores multiple dualities and emergent symmetries at deconfined quantum critical points in 2D antiferromagnets, proposing new theoretical descriptions and testing their implications for critical phenomena.

Contribution

It introduces new dualities and emergent symmetries for deconfined QCPs, linking them to surface states of 3+1D topological phases and providing numerical tests.

Findings

Duality between easy-plane deconfined QCP and Nf=2 QED.

Emergence of SO(5) symmetry rotating Néel and VBS orders.

Numerical evidence supporting the proposed dualities.

Abstract

The deconfined quantum critical point (QCP), separating the N\'eel and valence bond solid phases in a 2D antiferromagnet, was proposed as an example of $2+1$D criticality fundamentally different from standard Landau-Ginzburg-Wilson-Fisher {criticality}. In this work we present multiple equivalent descriptions of deconfined QCPs, and use these to address the possibility of enlarged emergent symmetries in the low energy limit. The easy-plane deconfined QCP, besides its previously discussed self-duality, is dual to $N_f = 2$ fermionic quantum electrodynamics (QED), which has its own self-duality and hence may have an O(4)$\times Z_2^T$ symmetry. We propose several dualities for the deconfined QCP with ${\mathrm{SU}(2)}$ spin symmetry which together make natural the emergence of a previously suggested $SO(5)$ symmetry rotating the N\'eel and VBS orders. These emergent symmetries are implemented anomalously. The associated infra-red theories can also be viewed as surface descriptions of 3+1D topological paramagnets, giving further insight into the dualities. We describe a number of numerical tests of these dualities. We also discuss the possibility of "pseudocritical" behavior for deconfined critical points, and the meaning of the dualities and emergent symmetries in such a scenario.