Spectroscopic evidences for the spontaneous symmetry breaking at the $SO(5)$ deconfined critical point of $J$-$Q_3$ model

Shutao Liu; Yan Liu; Chengkang Zhou; Zhe Wang; Jie Lou; Changle Liu; Zheng Yan; Yan Chen

Paper

Spectroscopic evidences for the spontaneous symmetry breaking at the $SO(5)$ deconfined critical point of $J$-$Q_3$ model

Abstract

Recent numerical and theoretical studies on the two-dimensional

model suggests that the deconfined quantum critical point is actually a

-symmetry-enhanced first-order phase transition that is spontaneously broken to

. However, this conclusion has mainly relied on finite-size scaling of the entanglement entropy, lacking direct evidence from physical observables.} Here, we investigate the dynamical spectra of spin and bond operators at the deconfined critical point of the

model using large-scale quantum Monte Carlo simulations, and contrasting them with the well-established

Wilson-Fisher criticality in the

Heisenberg model. Although both models exhibit two gapless magnon modes in the Néel phase, their critical behaviors diverge strikingly. At the

critical point, the Higgs mode becomes gapless, yielding three gapless modes that reflect the full restoration of the

symmetry. {In the

model, we instead observe four gapless transverse modes at the either side of the transition. This spectral feature, together with the entanglement entropy results, provides direct evidence for the weakly first-order scenario that the deconfined quantum critical point exhibits an emergent

symmetry that spontaneously breaks to