Entanglement of low-energy excitations in Conformal Field Theory

Abstract

In a quantum critical chain, the scaling regime of the energy and momentum of the ground state and low lying excitations are described by conformal field theory (CFT). The same holds true for the von Neumann and Renyi entropies of the ground state, which display a universal logarithmic behaviour depending on the central charge. In this letter we generalize this result to those excited states of the chain that correspond to primary fields in CFT. It is shown that the n-th Renyi entropy is related to a 2n-point correlator of primary fields. We verify this statement for the critical XX and XXZ chains. This result uncovers a new link between quantum information theory and CFT.

arXiv comment4 pages, 3 figures

References in corpus (18)

• Entanglement Entropy and Quantum Field Theory
• Area laws for the entanglement entropy - a review
• Entanglement in quantum critical phenomena
• Entropy and Area
• Geometric and Renormalized Entropy in Conformal Field Theory
• Calculation of reduced density matrices from correlation functions
• Entanglement Renyi entropies in holographic theories
• Renormalization and tensor product states in spin chains and lattices
• Entanglement entropy of two disjoint intervals in conformal field theory
• Entanglement entropy of two disjoint intervals in conformal field theory II
• Parity effects in the scaling of block entanglement in gapless spin chains
• Mutual Information and Boson Radius in c=1 Critical Systems in One Dimension
• Entanglement entropy of two disjoint blocks in XY chains
• Entanglement entropy of excited states
• Entanglement entropy of two disjoint blocks in critical Ising models
• An area law for the entropy of low-energy states
• Universal corrections to scaling for block entanglement in spin-1/2 XX chains
• Finite Size Corrections to Entanglement in Quantum Critical Systems

Cited by in corpus (157)

• Thermodynamical Property of Entanglement Entropy for Excited States
• Symmetry-resolved entanglement in many-body systems
• Entanglement Temperature and Entanglement Entropy of Excited States
• Holographic Entanglement Entropy from 2d CFT: Heavy States and Local Quenches
• Quantum Entanglement of Local Operators in Conformal Field Theories
• Equipartition of the Entanglement Entropy
• The entanglement entropy of one-dimensional gases
• Eigenstate thermalization hypothesis (ETH) and integrability in quantum spin chains
• Quantum Dimension as Entanglement Entropy in 2D CFTs
• Quantum Entanglement of Localized Excited States at Finite Temperature
• Global characteristics of all eigenstates of local many-body Hamiltonians: participation ratio and entanglement entropy
• Out of equilibrium dynamics with Matrix Product States
• Entanglement of Local Operators in large N CFTs
• Entanglement Entropy of Non Unitary Conformal Field Theory
• Entanglement in non-unitary quantum critical spin chains
• Symmetry resolved entanglement entropy of excited states in a CFT
• Entanglement entropy dynamics of disordered quantum spin chains
• Entanglement entropy and superselection sectors I. Global symmetries
• Random matrices and entanglement entropy of trapped Fermi gases
• Modular Hamiltonian of Excited States in Conformal Field Theory
• Entanglement entropy and negativity of disjoint intervals in CFT: Some numerical extrapolations
• Entanglement Entropy Scaling Laws and Eigenstate Typicality in Free Fermion Systems
• Notes on Quantum Entanglement of Local Operators
• Symmetry resolved relative entropies and distances in conformal field theory
• Entanglement entropy of two disjoint intervals in c=1 theories
• Universal Thermal Corrections to Single Interval Entanglement Entropy for Conformal Field Theories
• Relative entropy of excited states in two dimensional conformal field theories
• Entanglement of excited states in critical spin chians
• Universal behavior of the Shannon mutual information of critical quantum chains
• Entanglement Content of Quasi-Particle Excitations
• Excited state entanglement in homogeneous fermionic chains
• Area law violation for the mutual information in a nonequilibrium steady state
• Entanglement Entropies in Conformal Systems with Boundaries
• Bound states and entanglement in the excited states of quantum spin chains
• Entanglement hamiltonians in 1D free lattice models after a global quantum quench
• Universal scaling of the logarithmic negativity in massive quantum field theory
• Rényi entropy of locally excited states with thermal and boundary effect in 2D CFTs
• The entanglement entropy of 1D systems in continuous and homogenous space
• Entanglement of midspectrum eigenstates of chaotic many-body systems: Reasons for deviation from random ensembles
• Conformal data and renormalization group flow in critical quantum spin chains using periodic uniform matrix product states
• Entanglement entropy of two disjoint intervals and the recursion formula for conformal blocks
• Entanglement entropies of minimal models from null-vectors
• Subsystem Trace Distance in Quantum Field Theory
• More on the rainbow chain: entanglement, space-time geometry and thermal states
• Estimating Quasi-long-range Order via Renyi Entropies
• Entanglement constant for conformal families
• Relative entropy of excited states in conformal field theories of arbitrary dimensions
• Higher spin entanglement entropy from CFT
• Note on Entanglement Temperature for Low Thermal Excited States in Higher Derivative Gravity
• Shell-Filling Effect in the Entanglement Entropies of Spinful Fermions
• Subsystem eigenstate thermalization hypothesis for entanglement entropy in CFT
• Conformal fields and operator product expansion in critical quantum spin chains
• Excited state entanglement in one dimensional quantum critical systems: Extensivity and the role of microscopic details
• Finite-size corrections of the Entanglement Entropy of critical quantum chains
• Renyi Entropy for Local Quenches in 2D CFTs from Numerical Conformal Blocks
• Bipartite entanglement entropy of the excited states of the free fermions and the harmonic oscillators
• Relative Entanglement Entropies in 1+1-dimensional conformal field theories
• Renyi Entropy and Parity Oscillations of the Anisotropic Spin-s Heisenberg Chains in a Magnetic Field
• Entanglement Content of Quantum Particle Excitations II. Disconnected Regions and Logarithmic Negativity
• Left-Right Entanglement Entropy of Boundary States
• Entanglement Content of Quantum Particle Excitations I. Free Field Theory
• Entanglement entropy after a partial projective measurement in $1+1$ dimensional conformal field theories: exact results
• Eigenstate entanglement: Crossover from the ground state to volume laws
• Bulk entanglement entropy in perturbative excited states
• Generalized entanglement entropies in two-dimensional conformal field theory
• New insights into the entanglement of disjoint blocks
• Entanglement and relative entropies for low-lying excited states in inhomogeneous one-dimensional quantum systems
• Subsystem trace distance in low-lying states of $(1+1)$-dimensional conformal field theories
• Conformal bootstrap to Rényi entropy in 2D Liouville and super-Liouville CFTs
• Gravitational anomalies, entanglement entropy, and flat-space holography
• Degenerate observables and the many Eigenstate Thermalization Hypotheses
• Entanglement evolution across defects in critical anisotropic Heisenberg chains
• Unusual area-law violation in random inhomogeneous systems
• Renyi entanglement entropies of descendant states in critical systems with boundaries: conformal field theory and spin chains
• Excitation Entanglement Entropy in 2d Conformal Field Theories
• SVD Entanglement Entropy
• Critical properties and Rényi entropies of the spin-3/2 XXZ chain
• Quantum Entanglement of Fermionic Local Operators
• Causal Evolutions of Bulk Local Excitations from CFT
• Note on Rényi entropy of 2D perturbed free fermions
• Entanglement Storage Units
• Entanglement in low-energy states of the random-hopping model
• Symmetry Resolved Entanglement of Excited States in Quantum Field Theory II: Numerics, Interacting Theories and Higher Dimensions
• Entanglement Content of Quantum Particle Excitations III. Graph Partition Functions
• Entanglement of several blocks in fermionic chains
• Looking at Shadows of Entanglement Wedges
• Generating Function for Tensor Network Diagrammatic Summation
• Corrections to universal Rényi entropy in quasiparticle excited states of quantum chains
• Entanglement Entropies of the quarter filled Hubbard model
• Entanglement of magnon excitations in spin chains
• Quantum Entanglement of Locally Excited States in Maxwell Theory
• Bulk entanglement entropy for photons and gravitons in AdS${}_3$
• On Holographic Entanglement Entropy with Second Order Excitations
• Universal Rényi Entropy of Quasiparticle Excitations
• Entanglement Entropy from the Truncated Conformal Space
• Massive Corrections to Entanglement in Minimal E8 Toda Field Theory
• Bootstrapping Quantum Extremal Surfaces I: The Area Operator
• Symmetry Resolved Measures in Quantum Field Theory: a Short Review
• Excited state Rényi entropy and subsystem distance in two-dimensional non-compact bosonic theory -- I. Single-particle states
• Quantum dimensions from local operator excitations in the Ising model
• A duality principle for the multi-block entanglement entropy of free fermion systems
• Entanglement Entropy of the Low-Lying Excited States and Critical Properties of an Exactly Solvable Two-Leg Spin Ladder with Three-Spin Interactions
• Adiabatic Tracking of a State: a New Route to Nonequilibrium Physics
• Universal entanglement and correlation measure in two-dimensional conformal field theories
• Excited state Rényi entropy and subsystem distance in two-dimensional non-compact bosonic theory. Part II. Multi-particle states
• Entanglement entropy after selective measurements in quantum chains
• Universal behavior of the Shannon mutual information in non-integrable self-dual quantum chains
• Entanglement entropy and boundary renormalization group flow - exact results in the Ising universality class
• Entanglement spreading after local fermionic excitations in the XXZ chain
• Post-Quantum Quench Growth of Renyi Entropies in Low Dimensional Continuum Bosonic Systems
• Entanglement entropy of the long-range Dyson hierarchical model
• Multi-boundary generalization of thermofield double states and their realization in critical quantum spin chains
• Entanglement Thermodynamics of the Generalized Charged BTZ Black Hole
• Entanglement Temperature in Non-conformal Cases
• Phase diagram of the alternating-spin Heisenberg chain with extra isotropic three-body exchange interactions
• Entanglement entropy of low-lying excitation in localized interacting system: Signature of Fock space delocalization
• Entanglement Entropy of Excited States in the Quantum Lifshitz Model
• Subsystem distances between quasiparticle excited states
• Radiation, entanglement and islands from a boundary local quench
• Symmetry Resolved Entanglement of Excited States in Quantum Field Theory III: Bosonic and Fermionic Negativity
• Entanglement and boundary entropy in quantum spin chains with arbitrary direction of the boundary magnetic fields
• Trace distance between fermionic Gaussian states from a truncation method
• Entanglement Entropy for Descendent Local Operators in 2D CFTs
• Entanglement Entropy in Excited States of the Quantum Lifshitz Model
• Entanglement Entropy and Modular Hamiltonian of free fermion with deformations on a torus
• Correspondence between Entanglement Growth and Probability Distribution of Quasi-Particles
• The Aharonov-Bohm Effect on Entanglement Entropy in Conformal Field Theory
• Correlation functions and quantum measures of descendant states
• Critical behavior of su(1|1) supersymmetric spin chains with long-range interactions
• Numerical calculations on the relative entanglement entropy in critical spin chains
• Entanglement entropy in quantum spin chains with broken parity number symmetry
• Rényi entropy and subsystem distances in finite size and thermal states in critical XY chains
• Zero-mode entanglement across a conformal defect
• Fourier-space entanglement of spin chains
• Scaling functions for eigenstate entanglement crossovers in harmonic lattices
• Entanglement and its evolution after a quench in the presence of an energy current
• Efficient Quantum Circuits based on the Quantum Natural Gradient
• Symmetric Orbifolds and Entanglement Entropy for Primary Excitations in Two Dimensional CFT
• Inhomogeneous Quantum Quenches of Conformal Field Theory with Boundaries
• Unravelling Holographic Entanglement Entropy in Higher Spin Theories
• Statistical mechanical mapping and maximum-likelihood thresholds for the surface code under generic single-qubit coherent errors
• The operator algebra of cyclic orbifolds
• Scaling of finite size effect of $\alpha$-Rényi entropy in disjointed intervals under dilation
• Unusual Corrections to the Scaling of the Entanglement Entropy of the Excited states in Conformal Field Theory
• On symmetry-resolved generalized entropies
• No eigenstate of the critical transverse-field Ising chain satisfies the area law
• Aspects of Entanglement Entropy in Algebraic Quantum Field Theory
• Entanglement content of kink excitations
• Thermal Correction to Entanglement Spectrum for Conformal Field Theories
• Holographic Entanglement Entropy for Excited States in Two Dimensional CFT
• Entanglement spreading after local and extended excitations in a free-fermion chain
• Entanglement distance between quantum states and its implications for density-matrix-renormalization-group study of degenerate ground-states
• Entanglement in descendants
• Geometric Rényi mutual information induced by localized particle excitations in quantum field theory
• Volume-law entanglement fragmentation of quasiparticles
• $2$-Rényi CCNR Negativity of Compact Boson for multiple disjoint intervals
• Excited states from local effective Hamiltonians of matrix product states and their entanglement spectrum transition