Deconfined quantum critical points: symmetries and dualities

TL;DR

The work builds a comprehensive web of dualities for 2+1D deconfined quantum critical points, linking bosonic NCCP1 theories to fermionic QED3 and QED–GN and revealing emergent SO(5) or O(4) symmetries at the IR fixed point. It highlights how these dualities can be understood via nonperturbative bulk–boundary constructions using 3+1D bosonic SPT phases, providing anomaly-consistent surface theories and explicit bulk realizations. The authors discuss symmetry constraints, stability against perturbations, and phase diagrams, and propose concrete numerical and bootstrap tests to validate the emergent symmetries and dualities, including the possibility of pseudocritical behavior. The results illuminate how deconfined criticality may be characterized by a rich symmetry structure and a network of equivalent descriptions, with broad implications for 2D quantum magnets, QED3 systems, and topological phases.

Abstract

The deconfined quantum critical point (QCP), separating the Néel 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 Néel 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.

Figures (3)

• Figure 2: Phase diagram near the $SO(5)$-invariant fixed point with perturbation of the form $\lambda_1(X_{11}+X_{22})+ \lambda_2 X_{55}$.
• Figure 3: Phase diagram near the $SO(5)$-invariant fixed point with perturbation of the form $-\tilde{\lambda}_1(|z_1|^2+|z_2|^2)+ \tilde{\lambda}_2 [(|z_1|^2-|z_2|^2)^2-\frac{1}{3}(|z_1|^2+|z_2|^2)^2]$. This is the natural perturbation to consider in the context of deconfined criticality in quantum magnets. The emergent $SO(5)$ symmetry requires that the slope of the lower transition line is twice that of the upper transition line.
• Figure 4: Phase diagram near the $SO(5)$-invariant fixed point with perturbation of the form $m_{\phi}\phi^2+m_{\psi}(\bar{\psi}_1\psi_1-\bar{\psi}_2\psi_2)$. This is the natural perturbation to consider in the context of QED$_3$--Gross-Neveu theory. The emergent $SO(5)$ symmetry predicts that the slope of the transition lines is related to the relative amplitude of the correlation functions of the two operators, Eq. (\ref{['eq:cpsq']})