Recent numerical and theoretical studies on the two-dimensional $J\text{−}{Q}_3$ model suggest that the deconfined quantum critical point is actually a $\mathrm{SO}\left(5\right)$-symmetry-enhanced first-order phase transition that is spontaneously broken to $\mathrm{O}\left(4\right)$. However, the precise nature of the transition remains under active discussion. Despite extensive studies based on static quantities and entanglement properties, its low-energy excitation spectrum has received comparatively less attention. Here we investigate the dynamical spectra of spin and bond operators at the deconfined critical point of the $J\text{−}{Q}_3$ model using large-scale quantum Monte Carlo simulations and contrast them with the well-established $\mathrm{O}\left(3\right)$ Wilson-Fisher criticality in the $J_1\text{−}{J}_2$ columnar dimerized Heisenberg model. Although both models exhibit two gapless magnon modes in the Néel phase, their critical behaviors diverge strikingly. At the $J_1\text{−}{J}_2$ critical point, the Higgs mode becomes gapless, yielding three gapless modes that reflect the complete restoration of the $\mathrm{O}\left(3\right)$ symmetry. In the $J\text{−}{Q}_3$ model, we instead observe transverse excitations associated with the Néel and VBS order-parameter fluctuations becoming gapless at the transition, a behavior consistent with the emergence of $\mathrm{SO}\left(5\right)$ symmetry. While transverse modes become gapless at the transition, the behavior of the longitudinal (Higgs) mode remains unresolved.

Close

PrevNext

View figure in article

• Phase transitions
• Square lattice
• Monte Carlo methods
• Spin lattice models