Entanglement Entropy in the O(N) model

Abstract

It is generally believed that in spatial dimension d > 1 the leading contribution to the entanglement entropy S = - tr rho_A log rho_A scales as the area of the boundary of subsystem A. The coefficient of this "area law" is non-universal. However, in the neighbourhood of a quantum critical point S is believed to possess subleading universal corrections. In the present work, we study the entanglement entropy in the quantum O(N) model in 1 < d < 3. We use an expansion in epsilon = 3-d to evaluate i) the universal geometric correction to S for an infinite cylinder divided along a circular boundary; ii) the universal correction to S due to a finite correlation length. Both corrections are different at the Wilson-Fisher and Gaussian fixed points, and the epsilon -> 0 limit of the Wilson-Fisher fixed point is distinct from the Gaussian fixed point. In addition, we compute the correlation length correction to the Renyi entropy S_n = (log tr rho^n_A)/(1-n) in epsilon and large-N expansions. For N -> infinity, this correction generally scales as N^2 rather than the naively expected N. Moreover, the Renyi entropy has a phase transition as a function of n for d close to 3.

40 pages, 10 figures

References in corpus (19)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Entanglement Entropy and Quantum Field Theory
• Aspects of Holographic Entanglement Entropy
• Entropy and Area
• Geometric and Renormalized Entropy in Conformal Field Theory
• Critical Phenomena and Renormalization-Group Theory
• Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
• Entanglement entropy, conformal invariance and extrinsic geometry
• The Theory of Boundary Critical Phenomena
• Universal terms for the entanglement entropy in 2+1 dimensions
• Quantum Criticality and Deconfinement in Phase Transitions Between Valence Bond Solids
• Entanglement and alpha entropies for a massive scalar field in two dimensions
• Entanglement Entropy and Twist Fields
• Quantum impurity dynamics in two-dimensional antiferromagnets and superconductors
• Universal entanglement entropy in 2D conformal quantum critical points
• Numerical study of entanglement entropy in SU(2) lattice gauge theory
• Entanglement Entropy in Critical Phenomena and Analogue Models of Quantum Gravity
• Entanglement entropy for a Dirac fermion in three dimensions: vertex contribution
• Valence bond solid order near impurities in two-dimensional quantum antiferromagnets

Cited by in corpus (152)

• Holographic Entanglement Entropy: An Overview
• Quantum entanglement in condensed matter systems
• Holographic c-theorems in arbitrary dimensions
• Entanglement entropy of black holes
• Measuring Renyi Entanglement Entropy with Quantum Monte Carlo
• Seeing a c-theorem with holography
• Hidden Fermi surfaces in compressible states of gauge-gravity duality
• Holographic Mutual Information is Monogamous
• Simulation of two-dimensional quantum systems using a tree tensor network that exploits the entropic area law
• Holographic Calculations of Renyi Entropy
• Holographic Fermi Surfaces and Entanglement Entropy
• Quantum Entanglement of Local Operators in Conformal Field Theories
• Entanglement from Charge Statistics: Exact Relations for Many-Body Systems
• A geometric proof of the equality between entanglement and edge spectra
• Entanglement entropy of critical spin liquids
• Quantum Monte Carlo calculation of entanglement Renyi entropies for generic quantum systems
• Entanglement at a Two-Dimensional Quantum Critical Point: a Numerical Linked Cluster Expansion Study
• How universal is the entanglement spectrum?
• Renyi Entropies for Free Field Theories
• Diagnostics of mixed-state topological order and breakdown of quantum memory
• Supersymmetric Renyi Entropy
• Finite Size Scaling of Mutual Information: A Scalable Simulation
• Bulk Emergence and the RG Flow of Entanglement Entropy
• Criticality and entanglement in random quantum systems
• Coherent and dissipative dynamics at quantum phase transitions
• Finite correlation length scaling with infinite projected entangled-pair states
• Rényi entropy of a line in two-dimensional Ising models
• Entanglement Wedge Cross Section from CFT: Dynamics of Local Operator Quench
• Random matrices and entanglement entropy of trapped Fermi gases
• Entanglement Entropy: A Perturbative Calculation
• Universal crossovers between entanglement entropy and thermal entropy
• Logarithmic terms in entanglement entropies of 2D quantum critical points and Shannon entropies of spin chains
• The critical O(N) CFT: Methods and conformal data
• Corner contribution to the entanglement entropy of an O(3) quantum critical point in 2+1 dimensions
• Entanglement spectrum of random-singlet quantum critical points
• Notes on Quantum Entanglement of Local Operators
• Entanglement entropies in free fermion gases for arbitrary dimension
• Holographic Phases of Renyi Entropies
• Symmetry resolved entanglement in two-dimensional systems via dimensional reduction
• Entanglement entropy scaling in the bilayer Heisenberg spin system
• Light Cone Bootstrap in General 2D CFTs and Entanglement from Light Cone Singularity
• Entanglement generation in periodically driven integrable systems: dynamical phase transitions and steady state
• Nonzero temperature Entanglement Negativity of quantum spin models: Area law, Linked Cluster Expansions and Sudden Death
• Entanglement Entropy for Relevant and Geometric Perturbations
• Entanglement entropy across the superfluid-insulator transition : a signature of bosonic criticality
• Thermal vs. Entanglement Entropy: A Measurement Protocol for Fermionic Atoms with a Quantum Gas Microscope
• Participation spectroscopy and entanglement Hamiltonian of quantum spin models
• Shape Dependence of Holographic Rényi Entropy in General Dimensions
• Entanglement scaling in two-dimensional gapless systems
• An Isotropic to Anisotropic Transition in a Fractional Quantum Hall State
• Entanglement in ground and excited states of gapped fermion systems and their relationship with fermi surface and thermodynamic equilibrium properties
• Singularity in Entanglement Negativity Across Finite Temperature Phase Transitions
• Entanglement Entropy in Scalar Field Theory
• Entanglement Entropy, OTOC and Bootstrap in 2D CFTs from Regge and Light Cone Limits of Multi-point Conformal Block
• Thermodynamic singularities in the entanglement entropy at a 2D quantum critical point
• Entanglement entropy of the $\nu =1/2$ composite fermion non-Fermi liquid state
• Universal behavior of a bipartite fidelity at quantum criticality
• Entanglement signatures of emergent Dirac fermions: kagome spin liquid & quantum criticality
• A Wang-Landau method for calculating Renyi entropies in finite-temperature quantum Monte Carlo simulations
• Higher-form symmetry breaking at Ising transitions
• Entanglement entropy of the large $N$ Wilson-Fisher conformal field theory
• Area terms in entanglement entropy
• Entanglement at a Two-Dimensional Quantum Critical Point: a T=0 Projector Quantum Monte Carlo Study
• A path integral Monte Carlo method for Rényi entanglement entropies
• Charged Renyi entropies and holographic superconductors
• Bounds on corner entanglement in quantum critical states
• Entanglement entropy of a Maxwell field on the sphere
• Machine learning discovery of new phases in programmable quantum simulator snapshots
• Scaling of Entanglement Entropy at 2D quantum Lifshitz fixed points and topological fluids
• Entanglement entropy between two coupled Tomonaga-Luttinger liquids
• Entanglement entropy, planar surfaces, and spectral functions
• Monodromy Defects from Hyperbolic Space
• Universal corner entanglement of Dirac fermions and gapless bosons from the continuum to the lattice
• Understanding the entanglement entropy and spectra of 2D quantum systems through arrays of coupled 1D chains
• Fluctuations and Entanglement spectrum in quantum Hall states
• Counting statistics for non-interacting fermions in a $d$-dimensional potential
• Monodromy Defects in Free Field Theories
• The fine structure of the entanglement entropy in the classical XY model
• Entanglement Entropy in Non-Relativistic Field Theories
• Structure of Quantum Entanglement at a Finite Temperature Critical Point
• Holographic Rényi Entropies at Finite Coupling
• Two-cylinder entanglement entropy under a twist
• Entanglement entropy in dynamic quantum-coherent conductors
• Quantum Entanglement of Fermionic Local Operators
• Scaling of entanglement entropy across Lifshitz transitions
• Entanglement entropy and the complex plane of replicas
• Measuring von Neumann entanglement entropies without wave functions
• The Renyi Entropy and the Multifractal Spectrum of Systems Near the Localization Transition
• Universal Behavior of Entanglement in 2D Quantum Critical Dimer Models
• Entanglement and classical fluctuations at finite-temperature critical points
• Scaling of entanglement in $2+1$-dimensional scale-invariant field theories
• Quantum Entanglement of Locally Excited States in Maxwell Theory
• Universal signatures of Dirac fermions in entanglement and charge fluctuations
• Density-Matrix Renormalization Group Study of Kitaev--Heisenberg Model on a Triangular Lattice
• Area law violations in a supersymmetric model
• Unusual Corrections to Scaling and Convergence of Universal Renyi Properties at Quantum Critical Points
• Capacity of entanglement and distribution of density matrix eigenvalues in gapless systems
• Particle partition entanglement of bosonic Luttinger liquids
• Cornering gapless quantum states via their torus entanglement
• Bootstrapping Quantum Extremal Surfaces I: The Area Operator
• Correlation functions on conical defects
• Quantum Critical Universality and Singular Corner Entanglement Entropy of Bilayer Heisenberg-Ising model
• Quantum Correlation with Sandwiched Relative Entropies: Advantageous as Order Parameter in Quantum Phase Transitions
• Wess-Zumino Consistency Condition for Entanglement Entropy
• Phase transitions in 3D gravity and fractal dimension
• Entanglement properties of the antiferromagnetic-singlet transition in the Hubbard model on bilayer square lattices
• On the entanglement across a cubic interface in 3+1 dimensions
• Holographic torus entanglement and its RG flow
• Entanglement and RG in the $O(N)$ vector model
• Entanglement Entropy of Coupled Conformal Field Theories and Fermi Liquids
• Sphere Renyi entropies
• Strong Coupling Expansion of the Entanglement Entropy of Yang-Mills Gauge Theories
• Entanglement Entropy of Fermions from Wigner Functions: Excited States and Open Quantum Systems
• Entanglement Entropy in Scalar Quantum Electrodynamics
• Renyi Entropy of Interacting Thermal Bosons in Large $N$ Approximation
• Entanglement entropy in scalar field theory and ${\mathbb{Z}}_M$ gauge theory on Feynman diagrams
• Entanglement sum rules in exactly solvable models
• Non-Gaussianity of Entanglement Entropy and Correlations of Composite Operators
• Wilsonian Effective Action and Entanglement Entropy
• Tracking the variation of entanglement Rényi negativity: a quantum Monte Carlo study
• Entanglement properties of Floquet Chern insulators
• An entropy perspective on the thermal crossover in a fermionic Hubbard chain
• Critical Scaling Behaviors of Entanglement Spectra
• The Edge of Entanglement: Getting the Boundary Right for Non-Minimally Coupled Scalar Fields
• The Aharonov-Bohm Effect on Entanglement Entropy in Conformal Field Theory
• A Rényi entropy perspective on topological order in classical toric code models
• Non-analyticity of holographic Rényi entropy in Lovelock gravity
• Closure of the entanglement gap at quantum criticality: The case of the Quantum Spherical Model
• On phase transitions in the Rényi entropies of 2+1-d large-N interacting vector models
• Entanglement entropies and fermion signs of critical metals
• Quantum Rényi entropy by optimal thermodynamic integration paths
• Entanglement gap, corners, and symmetry breaking
• Dynamical mean-field theory for Rényi entanglement entropy and mutual Information in Hubbard Model
• Instantons and Entanglement Entropy
• Universal Behavior in Entanglement Entropy Reveals Quantum Criticality and Underlying Symmetry Breaking
• Rényi Information flow in the Ising model with single-spin dynamics
• Entanglement entropy between real and virtual particles in ${\varphi }^4$ quantum field theory
• Exact renormalization group for wave functionals
• Entanglement entropy between virtual and real excitations in quantum electrodynamics
• Entanglement Entropy of $(2+1)$D Quantum Critical Points with Quenched Disorder: Dimensional Reduction Approach
• Entanglement entropy in low-energy field theories at finite chemical potential
• Entanglement in the Quantum Spherical Model -- a Review
• Building Entanglement Entropy out of Correlation Functions for Interacting Fermions
• Inspecting non-perturbative contributions to the Entanglement Entropy via wavefunctions
• Entanglement gap in 1D long-range quantum spherical models
• Rényi entropies for one-dimensional quantum systems with mixed boundary conditions
• Entanglement Entropy and Quantum Phase Transition in the $O(N)$ $\sigma$-model
• Second Rényi entropy and annulus partition function for one-dimensional quantum critical systems with boundaries
• The Area Term of the Entanglement Entropy of a Supersymmetric $O(N)$ Vector Model in Three Dimensions
• Extended Holographic Rényi Entropy and hyperbolic black hole with scalar hair
• Holographic entanglement renormalisation for fermionic quantum matter
• Boundary Renormalization Group Flow of Entanglement Entropy at a (2+1)-Dimensional Quantum Critical Point