Complex entanglement entropy for complex conformal field theory

Abstract

Conformal field theory underlies critical ground states of quantum many-body systems. While conventional conformal field theory is associated with positive central charges, nonunitary conformal field theory with complex-valued central charges has recently been recognized as physically relevant. Here, we demonstrate that complex-valued entanglement entropy characterizes complex conformal field theory and critical phenomena of open quantum many-body systems. This is based on non-Hermitian reduced density matrices constructed from the combination of right and left ground states. Applying the density matrix renormalization group to non-Hermitian systems, we numerically calculate the complex entanglement entropy of the non-Hermitian five-state Potts model, thereby confirming the scaling behavior predicted by complex conformal field theory.

11 pages, 5 figures

References in corpus (74)

• Entanglement Entropy and Quantum Field Theory
• Making Sense of Non-Hermitian Hamiltonians
• Entanglement in quantum critical phenomena
• Topological entanglement entropy
• Edge states and topological invariants of non-Hermitian systems
• Detecting topological order in a ground state wave function
• Scaling of Entanglement close to a Quantum Phase Transitions
• Entanglement entropy and conformal field theory
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Entanglement in a simple quantum phase transition
• The physics of exceptional points
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Entanglement spectrum of a topological phase in one dimension
• Evolution of Entanglement Entropy in One-Dimensional Systems
• Topological Origin of Non-Hermitian Skin Effects
• Time-dependence of correlation functions following a quantum quench
• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• Anomalous edge state in a non-Hermitian lattice
• Non-Bloch Band Theory of Non-Hermitian Systems
• The ITensor Software Library for Tensor Network Calculations
• Correspondence between winding numbers and skin modes in non-hermitian systems
• Measurement-Induced Phase Transitions in the Dynamics of Entanglement
• Quantum Zeno Effect and the Many-body Entanglement Transition
• Quantum Entanglement Growth Under Random Unitary Dynamics
• Measurement-driven entanglement transition in hybrid quantum circuits
• Ballistic spreading of entanglement in a diffusive nonintegrable system
• Biorthogonal Quantum Mechanics
• Measurement-induced criticality in random quantum circuits
• Random Quantum Circuits
• Unitary-projective entanglement dynamics
• Quantum Error Correction in Scrambling Dynamics and Measurement-Induced Phase Transition
• Dynamical purification phase transitions induced by quantum measurements
• Deconfined quantum critical points: symmetries and dualities
• Conformality Lost
• Walking, Weak first-order transitions, and Complex CFTs
• Entanglement entropy and the Berry phase in solid states
• Non-Hermitian Kondo effect in ultracold alkaline-earth atoms
• Entanglement spectrum and entropy in topological non-Hermitian systems and non-unitary conformal field theories
• Holographic Pseudo Entropy
• Walking, Weak first-order transitions, and Complex CFTs II. Two-dimensional Potts model at $Q>4$
• Pseudo Entropy in dS/CFT and Time-like Entanglement Entropy
• Timelike entanglement entropy
• Entanglement in non-unitary quantum critical spin chains
• Universal properties of dissipative Tomonaga-Luttinger liquids: Case study of a non-Hermitian XXZ spin chain
• de Sitter space, extremal surfaces and "time-entanglement"
• Exceptional Bound States and negative Entanglement Entropy
• The $O(N)$ Model in $4<d<6$: Instantons and Complex CFTs
• Pseudo Entropy in Free Quantum Field Theories
• Aspects of Pseudo Entropy in Field Theories
• Detecting signals of weakly first-order phase transitions in two-dimensional Potts models
• Rényi entropies and negative central charges in non-Hermitian quantum systems
• Symmetry-resolved entanglement in critical non-Hermitian systems
• Universal Entanglement Spectra of Gapped One-dimensional Field Theories
• AdS/BCFT with Brane-Localized Scalar Field
• Petermann factors and phase rigidities near exceptional points
• Phase Transitions of Ferromagnetic Potts Models on the Simple Cubic Lattice
• Conformality Loss, Walking, and 4D Complex Conformal Field Theories at Weak Coupling
• Entanglement Entropy of Non-Hermitian Free Fermions
• Entanglement Entropy of Non-Hermitian Eigenstates and the Ginibre Ensemble
• Calculation of higher-order moments by higher-order tensor renormalization group
• Holographic Complex Conformal Field Theories
• Constructible reality condition of pseudo entropy via pseudo-Hermiticity
• Shadow of complex fixed point: Approximate conformality of Q>4 Potts model
• SVD Entanglement Entropy
• Entanglement Phase Transition in Holographic Pseudo Entropy
• Diagnosing weakly first-order phase transitions by coupling to order parameters
• Complex fixed points of the non-Hermitian Kondo model in a Luttinger liquid
• Renormalization-group theory for cooling first-order phase transitions in Potts models
• Fixed point annihilation for a spin in a fluctuating field
• Entanglement Hamiltonian in the non-Hermitian SSH model
• Reclaiming the Lost Conformality in a non-Hermitian Quantum 5-state Potts Model
• Hidden Critical Points in the Two-Dimensional $O(n>2)$ model: Exact Numerical Study of a Complex Conformal Field Theory
• Matrix product state fixed points of non-Hermitian transfer matrices
• Unitarity of Symplectic Fermion in $\alpha$-vacua with Negative Central Charge

Cited by in corpus (3)

• Spiral renormalization group flow and universal entanglement spectrum of the non-Hermitian 5-state Potts model
• Lattice and PT symmetries in tensor-network renormalization group: Case study of a hard-square lattice gas model
• Asymptotic freedom, lost: Complex conformal field theory in the two-dimensional $O(N>2)$ nonlinear sigma model and its realization in Heisenberg spin chains