Diagnosing $SO(5)$ Symmetry and First-Order Transition in the $J-Q_3$ Model via Entanglement Entropy

Abstract

We study the scaling behavior of the Rényi entanglement entropy with smooth boundaries at the phase transition point of the two-dimensional $J-Q_3$ model. Using the recently developed scaling formula [Deng {\it et al.}, Phys. Rev. B {\textbf{108}, 125144 (2023)}], we find a subleading logarithmic term with a coefficient showing that the number of Goldstone modes is four, indicating the existence of the spontaneous symmetry breaking from an emergent $SO(5)$ to $O(4)$ in the thermodynamic limit, but restored in a finite size. This result shows that the believed deconfined quantum critical point of the $J-Q_3$ model is a weak first-order transition point. Our work provides a new way to distinguish a state with spontaneously broken continuous symmetry from a critical state. The method is particularly useful in identifying weak first-order phase transitions, which are hard to determine using conventional methods.

9 pages, 10 figures

References in corpus (19)

• "Deconfined" quantum critical points
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Seeing a c-theorem with holography
• Scaling in the Fan of an Unconventional Quantum Critical Point
• Universal terms for the entanglement entropy in 2+1 dimensions
• From an Antiferromagnet to a Valence Bond Solid: Evidence for a First Order Phase Transition
• Scaling of entanglement entropy at deconfined quantum criticality
• Dirac Fermions with Competing Orders: Non-Landau Transition with Emergent Symmetry
• Proximate deconfined quantum critical point in SrCu2(BO3)2
• Entanglement entropy scaling in the bilayer Heisenberg spin system
• Measuring Rényi entanglement entropy with high efficiency and precision in quantum Monte Carlo simulations
• Transitions to valence-bond solid order in a honeycomb lattice antiferromagnet
• Scaling of disorder operator at deconfined quantum criticality
• Metallic and Deconfined Quantum Criticality in Dirac Systems
• Extracting subleading corrections in entanglement entropy at quantum phase transitions
• Diagnosing weakly first-order phase transitions by coupling to order parameters
• Nonequilibrium dynamics in deconfined quantum critical point revealed by imaginary-time evolution
• Improved scaling of the entanglement entropy of quantum antiferromagnetic Heisenberg systems

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