Conformal Operator Flows of the Deconfined Quantum Criticality from $\mathrm{SO}(5)$ to $\mathrm{O}(4)$

TL;DR

This paper investigates the deconfined quantum critical point (DQCP) transitioning from SO(5) to O(4) symmetry, using fuzzy sphere regularization to analyze conformal operator flows and reveal the nature of pseudo-criticality.

Contribution

It introduces a fuzzy sphere regularization approach to study the RG flow of conformal operators at the DQCP, uncovering the operator content and the persistence of scalar operators across symmetry transitions.

Findings

Identification of O(4) primaries from SO(5) primaries.

Evidence of a relevant scalar operator supporting pseudo-criticality.

Demonstration of fuzzy sphere scheme as a tool for RG flow analysis.

Abstract

The deconfined quantum critical point (DQCP), which separates two distinct symmetry-broken phases, was conjectured to be an example of (2+1)D criticality beyond the standard Landau-Ginzburg-Wilson paradigm. However, this hypothesis has been met with challenges and remains elusive. Here, we perform a systematic study of a microscopic model realizing the DQCP with a global symmetry tunable from $\mathrm{SO}(5)$ to $\mathrm{O}(4)$. Through the lens of fuzzy sphere regularization, we uncover the key information on the renormalization group flow of conformal operators. We reveal O(4) primaries decomposed from original SO(5) primaries by tracing conformal operator content and identifying the ``avoided level crossing'' in the operator flows. In particular, we find that the existence of a scalar operator, in support of the nature of pseudo-criticality, remains relevant, persisting from $\mathrm{SO}(5)$ to $\mathrm{O}(4)$ DQCP. This work not only uncovers the nature of O(4) DQCP but also demonstrates that the fuzzy sphere scheme offers a unique perspective on the renormalization group flow of operators in the study of critical phenomena.