Entanglement Entropy of Non Unitary Conformal Field Theory

Abstract

In this letter we show that the Rényi entanglement entropy of a region of large size $\ell$ in a one-dimensional critical model whose ground state breaks conformal invariance (such as in those described by non-unitary conformal field theories), behaves as $S_n\sim \frac{c_{\mathrm{eff}}(n+1)}{6n}\log \ell$, where $c_{\mathrm{eff}}=c-24\Delta >0$ is the effective central charge, $c$ (which may be negative) is the central charge of the conformal field theory and $\Delta \ne 0$ is the lowest holomorphic conformal dimension in the theory. We also obtain results for models with boundaries, and with a large but finite correlation length, and we show that if the lowest conformal eigenspace is logarithmic ($L_0=\Delta I+N$ with $N$ nilpotent), then there is an additional term proportional to $\log (\log \ell )$. These results generalize the well known expressions for unitary models. We provide a general proof, and report on numerical evidence for a non-unitary spin chain and an analytical computation using the corner transfer matrix method for a non-unitary lattice model. We use a new algebraic technique for studying the branching that arises within the replica approach, and find a new expression for the entanglement entropy in terms of correlation functions of twist fields for non-unitary models.

arXiv comment5 pages, 2 figures. Revised version including new derivation of the EE of logarithmic CFT. To appear in J. Phys. A. (fast track communications)

References in corpus (43)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Concentrating Partial Entanglement by Local Operations
• Making Sense of Non-Hermitian Hamiltonians
• Area laws for the entanglement entropy - a review
• Entanglement in quantum critical phenomena
• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• Geometric and Renormalized Entropy in Conformal Field Theory
• Evolution of Entanglement Entropy in One-Dimensional Systems
• Controlling Spin Exchange Interactions of Ultracold Atoms in Optical Lattices
• Conditions for a class of entanglement transformations
• Pseudo-Hermitian Representation of Quantum Mechanics
• A class of quantum many-body states that can be efficiently simulated
• Scaling Theory of the Integer Quantum Hall Effect
• Logarithmic Operators in Conformal Field Theory
• Counterflow Superfluidity of Two-Species Ultracold Atoms in a Commensurate Optical Lattice
• Entanglement negativity in quantum field theory
• Entanglement-assisted local manipulation of pure quantum states
• Form factors of branch-point twist fields in quantum integrable models and entanglement entropy
• Optical realization of relativistic non-Hermitian quantum mechanics
• Entanglement of low-energy excitations in Conformal Field Theory
• Controlling Correlated Tunneling and Superexchange Interactions with AC-Driven Optical Lattices
• The Magnetic Spin Ladder (C_{5}H_{12}N)_{2}CuBr_{4}: High Field Magnetization and Scaling Near Quantum Criticality
• On the definition of a unique effective temperature for non-equilibrium critical systems
• Systematic approach to cyclic orbifolds
• Entanglement Entropy, decoherence, and quantum phase transition of a dissipative two-level system
• Direct Observation of Magnon Fractionalization in the Quantum Spin Ladder
• Non-unitary Conformal Field Theory and Logarithmic Operators for Disordered Systems
• Necessary and Sufficient Conditions for the Trumping Relation
• Catalytic Conversion Probabilities for Bipartite Pure States
• PT Symmetry on the Lattice: The Quantum Group Invariant XXZ Spin-Chain
• Spin dynamics for bosons in an optical lattice
• c-Theorem for Disordered Systems
• Non-Hermitian Hamiltonians with real eigenvalues coupled to electric fields: from the time-independent to the time dependent quantum mechanical formulation
• Shell-Filling Effect in the Entanglement Entropies of Spinful Fermions
• PT-symmetric deformations of integrable models
• Time-integrated observables as order parameters for dynamical phase transitions in closed quantum systems
• Permutation operators, entanglement entropy, and the XXZ spin chain in the limit Δ-> -1
• Non compact conformal field theory and the a_2^{(2)} (Izergin-Korepin) model in regime III
• Spectra of non-hermitian quantum spin chains describing boundary induced phase transitions
• Completeness of ``Good'' Bethe Ansatz Solutions of a Quantum Group Invariant Heisenberg Model
• Entanglement Entropy for Logarithmic Conformal Field Theory
• Non-Hermitian Quantum Annealing in the Antiferromagnetic Ising Chain
• Cumulants of time-integrated observables of closed quantum systems and PT-symmetry, with an application to the quantum Ising chain

Cited by in corpus (60)

• Non-Hermitian Physics
• Measurement-Induced Entanglement Transitions in the Quantum Ising Chain: From Infinite to Zero Clicks
• Equipartition of the Entanglement Entropy
• Entanglement spectrum and entropy in topological non-Hermitian systems and non-unitary conformal field theories
• Entanglement and symmetry resolution in two dimensional free quantum field theories
• Physics at the entangling surface
• Entanglement in non-unitary quantum critical spin chains
• Universal properties of dissipative Tomonaga-Luttinger liquids: Case study of a non-Hermitian XXZ spin chain
• Correlation Lengths and Topological Entanglement Entropies of Unitary and Non-Unitary Fractional Quantum Hall Wavefunctions
• Finite-size corrections in critical symmetry-resolved entanglement
• Entanglement Content of Quasi-Particle Excitations
• Branch Point Twist Field Form Factors in the sine-Gordon Model II: Composite Twist Fields and Symmetry Resolved Entanglement
• Branch Point Twist Field Correlators in the Massive Free Boson Theory
• Universal scaling of the logarithmic negativity in massive quantum field theory
• Rényi entropies and negative central charges in non-Hermitian quantum systems
• Entanglement entropies of minimal models from null-vectors
• Biorthogonal quantum criticality in non-Hermitian many-body systems
• Symmetry-resolved entanglement in critical non-Hermitian systems
• Entanglement Entropy of Non-Unitary Integrable Quantum Field Theory
• Entanglement of the $3$-State Potts Model via Form Factor Bootstrap: Total and Symmetry Resolved Entropies
• Symmetry Resolved Entanglement of Excited States in Quantum Field Theory I: Free Theories, Twist Fields and Qubits
• Entanglement Content of Quantum Particle Excitations I. Free Field Theory
• Correlations at PT-symmetric quantum critical point
• Irreversibility of the renormalization group flow in non-unitary quantum field theory
• Entanglement Entropy of Non-Hermitian Eigenstates and the Ginibre Ensemble
• Renyi entanglement entropies of descendant states in critical systems with boundaries: conformal field theory and spin chains
• Deterministic chaos and fractal entropy scaling in Floquet CFT
• Exact hydrodynamic description of symmetry-resolved Rényi entropies after a quantum quench
• On $d{S}_4$ extremal surfaces and entanglement entropy in some ghost CFTs
• Entanglement, non-Hermiticity, and duality
• 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 Entropy from Corner Transfer Matrix in Forrester Baxter non-unitary RSOS models
• Two-Point Functions of Composite Twist Fields in the Ising Field Theory
• Entanglement Entropy from the Truncated Conformal Space
• Symmetry Resolved Measures in Quantum Field Theory: a Short Review
• Massive Corrections to Entanglement in Minimal E8 Toda Field Theory
• Quantum entanglement and non-Hermiticity in free-fermion systems
• Engineering Yang-Lee anyons via Majorana bound states
• Many-body entanglement and spectral clusters in the extended hard-core bosonic Hatano-Nelson model
• RSOS Quantum Chains Associated with Off-Critical Minimal Models and ${\mathbb{Z}}_n$ Parafermions
• Symmetry Resolved Entanglement of Excited States in Quantum Field Theory III: Bosonic and Fermionic Negativity
• Matrix product state fixed points of non-Hermitian transfer matrices
• Sublogarithmic behaviour of the entanglement entropy in fermionic chains
• Probing Conformal Invariant of Non-unitary Two-Dimensional Systems by Central Spin Decoherence
• Dynamical signatures of the Yang-Lee edge singularity in non-Hermitian systems
• On the Shape of Things: From holography to elastica
• Unitarity of Symplectic Fermion in $\alpha$-vacua with Negative Central Charge
• Electric conductivity in non-Hermitian holography
• Mimicking quantum correlation of a long-range Hamiltonian by finite-range interactions
• Quantum Information Aspects on Bulk and Nano Interacting Fermi System: Spin-Space Density Matrix Approach
• Two-point boundary correlation functions of dense loop models
• Einstein's equations and the pseudo-entropy of pseudo-Riemannian information manifolds
• The operator algebra of cyclic orbifolds
• Entanglement Entropy in Integrable Field Theories with Line Defects I. Topological Defect
• Entanglement Rényi entropies in celestial holography
• Bound energy, entanglement and identifying critical points in 1D long-range Kitaev model
• Rényi entropies for one-dimensional quantum systems with mixed boundary conditions
• Second Rényi entropy and annulus partition function for one-dimensional quantum critical systems with boundaries
• Time Evolution of the Symmetry Resolved Entanglement Entropy after a Mass Quench