Entanglement entropy and deconfined criticality: emergent SO(5) symmetry and proper lattice bipartition

Abstract

We study the Rényi entanglement entropy (EE) of the two-dimensional $J$-$Q$ model, the emblematic quantum spin model of deconfined criticality at the phase transition between antiferromagnetic and valence-bond-solid ground states. State-of-the-art quantum Monte Carlo calculations of the EE reveal critical corner contributions that scale logarithmically with the system size, with a coefficient in remarkable agreement with the form expected from a large-$N$ conformal field theory with SO($N=5$) symmetry. However, details of the bipartition of the lattice are crucial in order to observe this behavior. If the subsystem for the reduced density matrix does not properly accommodate valence-bond fluctuations, logarithmic contributions appear even for corner-less bipartitions. We here use a $45^{\circ }$ tilted cut on the square lattice. Beyond supporting an SO($5$) deconfined quantum critical point, our results for both the regular and tilted cuts demonstrate important microscopic aspects of the EE that are not captured by conformal field theory.

arXiv comment4.5 pages, 3 figures + supplemental material. Added corner subtraction to supplement

References in corpus (61)

• Entanglement Entropy and Quantum Field Theory
• Entanglement in quantum critical phenomena
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Axion Cosmology
• Entropy and Area
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• "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
• Computational Studies of Quantum Spin Systems
• Measuring Renyi Entanglement Entropy with Quantum Monte Carlo
• Universality of Entropy Scaling in 1D Gap-less Models
• Deconfined quantum critical points: symmetries and dualities
• Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
• Topological Entanglement Entropy of a Bose-Hubbard Spin Liquid
• Quantum criticality with two length scales
• 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
• Continuous quantum phase transition between an antiferromagnet and a valence-bond-solid in two dimensions; evidence for logarithmic corrections to scaling
• Emergent $SO(5)$ Symmetry at the Néel to Valence-Bond-Solid Transition
• Deconfined Quantum Criticality, Scaling Violations, and Classical Loop Models
• AdS/CFT and Strong Subadditivity of Entanglement Entropy
• Deconfined quantum criticality and Neel order via dimer disorder
• Many-body spin Berry phases emerging from the $\pi$-flux state: antiferromagnetic/valence-bond-solid competition
• A lattice model for the SU(N) Neel-VBS quantum phase transition at large N
• From an Antiferromagnet to a Valence Bond Solid: Evidence for a First Order Phase Transition
• Anomalies in the Entanglement Properties of the Square Lattice Heisenberg Model
• Quantum Monte Carlo calculation of entanglement Renyi entropies for generic quantum systems
• Fate of CP(N-1) fixed points with q-monopoles
• Numerical study of entanglement entropy in SU(2) lattice gauge theory
• Deconfined criticality flow in the Heisenberg model with ring-exchange interactions
• Possibility of Deconfined Criticality in SU(N) Heisenberg Models at Small N
• Entanglement at a Two-Dimensional Quantum Critical Point: a Numerical Linked Cluster Expansion Study
• Dynamical Signature of Fractionalization at the Deconfined Quantum Critical Point
• Entanglement Entropy of the Two-Dimensional Heisenberg Antiferromagnet
• Finite Size Scaling of Mutual Information: A Scalable Simulation
• Scaling of entanglement entropy at deconfined quantum criticality
• Corner contribution to the entanglement entropy of an O(3) quantum critical point in 2+1 dimensions
• Proximate deconfined quantum critical point in SrCu2(BO3)2
• Entanglement entropy scaling in the bilayer Heisenberg spin system
• Finite-size scaling and boundary effects in two-dimensional valence-bond-solids
• Entanglement entropy from nonequilibrium work
• Multicritical deconfined quantum-criticality and Lifshitz point of a helical valence-bond phase
• Thermodynamic singularities in the entanglement entropy at a 2D quantum critical point
• Entanglement entropy of the large $N$ Wilson-Fisher conformal field theory
• Out-of-equilibrium protocol for Rényi entropies via the Jarzynski equality
• Consistent scaling exponents at the deconfined quantum-critical point
• Level spectroscopy in a two-dimensional quantum magnet: Linearly dispersing spinons at the deconfined quantum critical point
• Detecting Goldstone Modes with Entanglement Entropy
• Universal corner entanglement of Dirac fermions and gapless bosons from the continuum to the lattice
• Valence-bond solids, vestigial order, and emergent SO(5) symmetry in a two-dimensional quantum magnet
• Universal features of entanglement entropy in the honeycomb Hubbard model
• Diagnosing $SO(5)$ Symmetry and First-Order Transition in the $J-Q_3$ Model via Entanglement Entropy
• Extracting subleading corrections in entanglement entropy at quantum phase transitions
• Diagnosing weakly first-order phase transitions by coupling to order parameters
• Correlations and entanglement in quantum critical bilayer and necklace XY models
• Kagome model for a ${\mathbb{Z}}_2$ quantum spin liquid
• Improved scaling of the entanglement entropy of quantum antiferromagnetic Heisenberg systems

Cited by in corpus (15)

• Evolution of entanglement entropy at SU($N$) deconfined quantum critical points
• Non-equilibrium quantum Monte Carlo algorithm for stabilizer Renyi entropy in spin systems
• Entanglement Microscopy: Tomography and Entanglement Measures via Quantum Monte Carlo
• Three-dimensional Abelian and non-Abelian gauge Higgs theories
• Equilibration of Topological Defects Near the Deconfined Quantum Multicritical Point
• Bipartite Fluctuations of Critical Fermi Surfaces
• Universal Behavior in Entanglement Entropy Reveals Quantum Criticality and Underlying Symmetry Breaking
• Topological physics in quantum critical systems
• Extracting Universal Corner Entanglement Entropy during the Quantum Monte Carlo Simulation
• Deconfined quantum criticality in a frustrated Haldane chain with single-ion anisotropy
• Deconfined criticality as intrinsically gapless topological state in one dimension
• Continuous order-to-order quantum phase transitions from fixed-point annihilation
• Exploring the limit of the Lattice-Bisognano-Wichmann form describing the Entanglement Hamiltonian: A quantum Monte Carlo study
• Deconfined pseudocriticality in a model spin-1 quantum antiferromagnet
• O(5) multicriticality in the 3D two flavor SU(2) lattice gauge Higgs model