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.

arXiv comment9 pages, 10 figures

References in corpus (46)

• "Deconfined" quantum critical points
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Quantum Monte Carlo with Directed Loops
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Computational Studies of Quantum Spin Systems
• Finite-Size Scaling of the Ground State Parameters of the Two-Dimensional Heisenberg Model
• Seeing a c-theorem with holography
• Quantum criticality with two length scales
• Finite size and temperature effects in the AF Heisenberg model
• Competing orders, non-linear sigma models, and topological terms in quantum magnets
• Scaling in the Fan of an Unconventional Quantum Critical Point
• Universal terms for the entanglement entropy in 2+1 dimensions
• Antiferromagnetic to valence-bond-soild transitions in two-dimensional SU(N) Heisenberg models with multi-spin interactions
• Emergent $SO(5)$ Symmetry at the Néel to Valence-Bond-Solid Transition
• Deconfined Quantum Criticality, Scaling Violations, and Classical Loop Models
• Loop updates for variational and projector quantum Monte Carlo simulations in the valence-bond basis
• From an Antiferromagnet to a Valence Bond Solid: Evidence for a First Order Phase Transition
• Deconfined criticality flow in the Heisenberg model with ring-exchange interactions
• Possibility of Deconfined Criticality in SU(N) Heisenberg Models at Small N
• Conformal Bootstrap Dashing Hopes of Emergent Symmetry
• Ground state projection of quantum spin systems in the valence bond basis
• A theory of deconfined pseudo-criticality
• Confinement transition of ${\mathbb{Z}}_2$ gauge theories coupled to massless fermions: emergent QCD${}_3$ and $SO(5)$ symmetry
• Scaling of entanglement entropy at deconfined quantum criticality
• Superconductivity from the Condensation of Topological Defects in a Quantum Spin-Hall Insulator
• Dirac Fermions with Competing Orders: Non-Landau Transition with Emergent Symmetry
• Note on Wess-Zumino-Witten models and quasiuniversality in 2+1 dimensions
• 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
• Symmetry enhanced first-order phase transition in a two-dimensional quantum magnet
• Entanglement entropy from nonequilibrium work
• Multicritical deconfined quantum-criticality and Lifshitz point of a helical valence-bond phase
• Transitions to valence-bond solid order in a honeycomb lattice antiferromagnet
• Scaling of disorder operator at deconfined quantum criticality
• Quantum criticality in SU(3) and SU(4) anti-ferromagnets
• Out-of-equilibrium protocol for Rényi entropies via the Jarzynski equality
• Consistent scaling exponents at the deconfined quantum-critical point
• Detecting Goldstone Modes with Entanglement Entropy
• Valence-bond solids, vestigial order, and emergent SO(5) symmetry in a two-dimensional quantum magnet
• 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
• Anomalous finite size spectrum in the S=1/2 two dimensional Heisenberg model

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