Extracting subleading corrections in entanglement entropy at quantum phase transitions

Abstract

We systematically investigate the finite size scaling behavior of the Rényi entanglement entropy (EE) of several representative 2d quantum many-body systems between a subregion and its complement, with smooth boundaries as well as boundaries with corners. In order to reveal the subleading correction, we investigate the quantity ``subtracted EE" $S^s(l)=S(2l)-2S(l)$ for each model, which is designed to cancel out the leading perimeter law. We find that $(1)$ for a spin-1/2 model on a 2d square lattice whose ground state is the Neel order, the coefficient of the logarithmic correction to the perimeter law is consistent with the prediction based on the Goldstone modes; $(2)$ for the $(2+1)d$ O(3) Wilson-Fisher quantum critical point (QCP), realized with the bilayer antiferromagnetic Heisenberg model, a logarithmic subleading correction exists when there is sharp corner of the subregion, but for subregion with a smooth boundary our data suggests the absence of the logarithmic correction to the best of our efforts; $(3)$ for the $(2+1)d$ SU(2) J-Q${}_2$ and J-Q${}_3$ model for the deconfined quantum critical point (DQCP), we find a logarithmic correction for the EE even with smooth boundary.

References in corpus (84)

• A nonequilibrium equality for free energy differences
• Entanglement Entropy and Quantum Field Theory
• Geometric and Renormalized Entropy in Conformal Field Theory
• "Deconfined" quantum critical points
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Quantum Monte Carlo with Directed Loops
• Quantum entanglement in condensed matter systems
• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Stochastic series expansion method with operator-loop update
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Deconfined quantum critical points: symmetries and dualities
• Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
• Quantum criticality with two length scales
• Competing orders, non-linear sigma models, and topological terms in quantum magnets
• 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
• Order-Disorder Transition in a Two-Layer Quantum Antiferromagnet
• Emergent $SO(5)$ Symmetry at the Néel to Valence-Bond-Solid Transition
• Universality of corner entanglement in conformal field theories
• Deconfined Quantum Criticality, Scaling Violations, and Classical Loop Models
• AdS/CFT and Strong Subadditivity of Entanglement Entropy
• Observation of a 4-spin Plaquette Singlet State in the Shastry-Sutherland compound SrCu2(BO3)2
• Deconfined quantum criticality and Neel order via dimer disorder
• Anomalies in the Entanglement Properties of the Square Lattice Heisenberg Model
• Duality between the deconfined quantum-critical point and the bosonic topological transition
• Fate of CP(N-1) fixed points with q-monopoles
• Deconfined criticality flow in the Heisenberg model with ring-exchange interactions
• Possibility of Deconfined Criticality in SU(N) Heisenberg Models at Small N
• Néel to valence-bond solid transition on the honeycomb lattice: Evidence for deconfined criticality
• Conformal Bootstrap Dashing Hopes of Emergent Symmetry
• Entanglement at a Two-Dimensional Quantum Critical Point: a Numerical Linked Cluster Expansion Study
• Quantum phases of SrCu2(BO3)2 from high-pressure thermodynamics
• Dynamical Signature of Fractionalization at the Deconfined Quantum Critical Point
• A theory of deconfined pseudo-criticality
• Monte Carlo Study of Lattice Compact Quantum Electrodynamics with Fermionic Matter: the Parent State of Quantum Phases
• Superconductivity from the Condensation of Topological Defects in a Quantum Spin-Hall Insulator
• Scaling of entanglement entropy at deconfined quantum criticality
• Deconfined quantum critical point in one dimension
• Note on Wess-Zumino-Witten models and quasiuniversality in 2+1 dimensions
• 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 of Systems with Spontaneously Broken Continuous Symmetry
• Entanglement entropy scaling in the bilayer Heisenberg spin system
• Shape Dependence of Entanglement Entropy in Conformal Field Theories
• Impurity spin texture at a deconfined quantum critical point
• Measuring Rényi entanglement entropy with high efficiency and precision in quantum Monte Carlo simulations
• Emergent Symmetry and Conserved Current at a One Dimensional Incarnation of Deconfined Quantum Critical Point
• Dynamical structure factors and excitation modes of the bilayer Heisenberg model
• Entanglement entropy from nonequilibrium work
• Multicritical deconfined quantum-criticality and Lifshitz point of a helical valence-bond phase
• Emmy Noether looks at the deconfined quantum critical point
• Scaling of disorder operator at deconfined quantum criticality
• Continuous easy-plane deconfined phase transition on the kagome lattice
• Universal Features of Higher-Form Symmetries at Phase Transitions
• Emergent SO(5) symmetry at the columnar ordering transition in the classical cubic dimer model
• Higher-form symmetry breaking at Ising transitions
• The $\mathrm{SO}(5)$ Deconfined Phase Transition under the Fuzzy Sphere Microscope: Approximate Conformal Symmetry, Pseudo-Criticality, and Operator Spectrum
• Fermion disorder operator at Gross-Neveu and deconfined quantum criticalities
• Scaling of disorder operator at $(2+1)d$ U(1) quantum criticality
• Out-of-equilibrium protocol for Rényi entropies via the Jarzynski equality
• Consistent scaling exponents at the deconfined quantum-critical point
• Bounds on corner entanglement in quantum critical states
• Unconventional Quantum Critical Points
• Detecting Goldstone Modes with Entanglement Entropy
• Universal corner entanglement of Dirac fermions and gapless bosons from the continuum to the lattice
• Topological Disorder Parameter
• Unconventional Superconducting Quantum Criticality in Monolayer WTe2
• Universal features of entanglement entropy in the honeycomb Hubbard model
• Entanglement entropies of the $J_1-J_2$ Heisenberg antiferromagnet on the square lattice
• Two-cylinder entanglement entropy under a twist
• Positivity, entanglement entropy, and minimal surfaces
• Phases of (2+1)D SO(5) non-linear sigma model with a topological term on a sphere: multicritical point and disorder phase
• Metallic and Deconfined Quantum Criticality in Dirac Systems
• Dirac fermions with plaquette interactions. I. SU(2) phase diagram with Gross-Neveu and deconfined quantum criticalities
• Stable computation of entanglement entropy for 2D interacting fermion systems
• Measuring von Neumann entanglement entropies without wave functions
• New easy-plane ${\mathbb{CP}}^{N-1}$ fixed points
• Disorder Operator and Rényi Entanglement Entropy of Symmetric Mass Generation
• Incremental SWAP Operator for Entanglement Entropy: Application for Exponential Observables in Quantum Monte Carlo Simulation
• An integral algorithm of exponential observables for interacting fermions in quantum Monte Carlo simulation
• Improved scaling of the entanglement entropy of quantum antiferromagnetic Heisenberg systems
• The teaching from entanglement: 2D SU(2) antiferromagnet to valence bond solid deconfined quantum critical points are not conformal
• Deconfined quantum critical points: a review

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• Unconventional Scalings of Quantum Entropies in Long-Range Heisenberg Chains
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• Monte Carlo Simulation of Operator Dynamics and Entanglement in Dual-Unitary Circuits
• Symmetrizing the Constraints -- Density Matrix Renormalization Group for Constrained Lattice Models
• Accessing Excitation of Many-body Systems via Single-Mode Approximation within Quantum Monte Carlo Simulations
• Multiparty Entanglement Microscopy of Quantum Ising models in 1d, 2d and 3d
• Exploring the limit of the Lattice-Bisognano-Wichmann form describing the Entanglement Hamiltonian: A quantum Monte Carlo study