Entanglement spectrum and entropy in topological non-Hermitian systems and non-unitary conformal field theories

Abstract

We propose a method of computing and studying entanglement quantities in non-Hermitian systems by use of a biorthogonal basis. We find that the entanglement spectrum characterizes the topological properties in terms of the existence of mid-gap states in the non-Hermitian Su-Schrieffer-Heeger (SSH) model with parity and time-reversal symmetry (PT symmetry) and the non-Hermitian Chern insulators. In addition, we find that at a critical point in the PT symmetric SSH model, the entanglement entropy has a logarithmic scaling with corresponding central charge $c=-2$. This critical point then is a free-fermion lattice realization of the non-unitary conformal field theory.

17 pages, 11 figures

References in corpus (51)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Entanglement Entropy and Quantum Field Theory
• Topological entanglement entropy
• Edge states and topological invariants of non-Hermitian systems
• Detecting topological order in a ground state wave function
• Aspects of Holographic Entanglement Entropy
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Topological phases of non-Hermitian systems
• Symmetry and Topology in Non-Hermitian Physics
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Entanglement spectrum of a topological phase in one dimension
• Topological Band Theory for Non-Hermitian Hamiltonians
• Anomalous edge state in a non-Hermitian lattice
• Non-Hermitian robust edge states in one-dimension: Anomalous localization and eigenspace condensation at exceptional points
• Holographic Entanglement Entropy: An Overview
• Reduced density matrices and entanglement entropy in free lattice models
• Complex Edge-State Phase Transitions in 1D Topological Laser Arrays
• Inversion Symmetric Topological Insulators
• Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Biorthogonal Quantum Mechanics
• Edge states and topological phases in non-Hermitian systems
• Topologically protected midgap states in complex photonic lattices
• Geometrical meaning of winding number and its characterization of topological phases in one-dimensional chiral non-Hermitian systems
• Density-Matrix Spectra of Solvable Fermionic Systems
• Non-Hermitian perspective of the band structure in heavy-fermion systems
• Exceptional rings in two-dimensional correlated systems with chiral symmetry
• Entanglement hamiltonians in two-dimensional conformal field theory
• Topological invariance and global Berry phase in non-Hermitian systems
• Symplectic Fermions
• Defining a bulk-edge correspondence for non-Hermitian Hamiltonians via singular-value decomposition
• Signatures of three coalescing eigenfunctions
• Anomalous helical edge states in a non-Hermitian Chern insulator
• Entanglement entropy and the Berry phase in solid states
• Parity-time-symmetric topological superconductor
• Topology and edge modes in quantum critical chains
• Relation between $\mathcal{P}\mathcal{T}$-symmetry breaking and topologically nontrivial phases in the SSH and Kitaev models
• Entanglement spectrum and symmetries in non-Hermitian fermionic non-interacting models
• Observation of emergent momentum-time skyrmions in parity-time-symmetric non-unitary quench dynamics
• Entanglement Entropy of Non Unitary Conformal Field Theory
• Entanglement in non-unitary quantum critical spin chains
• Completeness and Orthonormality in PT-symmetric Quantum Systems
• Entanglement entropies of minimal models from null-vectors
• Entanglement Entropy of Non-Unitary Integrable Quantum Field Theory
• Relating c<0 and c>0 Conformal Field Theories
• On $d{S}_4$ extremal surfaces and entanglement entropy in some ghost CFTs
• Exact description of coalescing eigenstates in open quantum systems in terms of microscopic Hamiltonian dynamics
• Symmetry-protected entangling boundary zero modes in crystalline topological insulators
• Entanglement Entropy from Corner Transfer Matrix in Forrester Baxter non-unitary RSOS models
• Topological edge states in the Su-Schrieffer-Heeger model subject to balanced particle gain and loss
• Ghost-spin chains, entanglement and $bc$-ghost CFTs

Cited by in corpus (116)

• Non-Hermitian Physics
• Non-Hermitian Topology and Exceptional-Point Geometries
• Critical non-Hermitian Skin Effect
• Higher-order non-Hermitian skin effect
• Topological Non-Hermitian skin effect
• Entanglement Phase Transition Induced by the Non-Hermitian Skin Effect
• Pseudo Entropy in dS/CFT and Time-like Entanglement Entropy
• Emergent Fermi surface in a many-body non-Hermitian Fermionic chain
• Many-body topology of non-Hermitian systems
• Topological Field Theory of Non-Hermitian Systems
• Volume-to-Area Law Entanglement Transition in a non-Hermitian Free Fermionic Chain
• Quantum anomaly, non-Hermitian skin effects, and entanglement entropy in open systems
• Universal properties of dissipative Tomonaga-Luttinger liquids: Case study of a non-Hermitian XXZ spin chain
• Floquet dynamical phase transition and entanglement spectrum
• Exceptional Bound States and negative Entanglement Entropy
• Non-Hermitian Bulk-Boundary Correspondence in Periodically Driven System
• Non-Hermitian Pseudo-Gaps
• Hunting for the non-Hermitian exceptional points with fidelity susceptibility
• Non-Hermitian Mott Skin Effect
• Rényi entropies and negative central charges in non-Hermitian quantum systems
• Universal competitive spectral scaling from the critical non-Hermitian skin effect
• General properties of fidelity in non-Hermitian quantum systems with PT symmetry
• Designing non-Hermitian real spectra through electrostatics
• Biorthogonal quantum criticality in non-Hermitian many-body systems
• Symmetry-resolved entanglement in critical non-Hermitian systems
• Non-Hermitian strongly interacting Dirac fermions: a quantum Monte-Carlo study
• Quantum Entanglement of Non-Hermitian Quasicrystals
• Non-Hermitian Squeezed Polarons
• Unconventional scaling at non-Hermitian critical points
• Observation of the non-Hermitian skin effect and Fermi skin on a digital quantum computer
• Bulk-boundary correspondence in point-gap topological phases
• Dynamics of entanglement after exceptional quantum quench
• Entanglement Spectrum Crossings Reveal non-Hermitian Dynamical Topology
• High-fidelity realization of the AKLT state on a NISQ-era quantum processor
• Entanglement Entropy of Non-Hermitian Free Fermions
• Correlations at PT-symmetric quantum critical point
• Entanglement Entropy of Non-Hermitian Eigenstates and the Ginibre Ensemble
• Classification of topological phases in one dimensional interacting non-Hermitian systems and emergent unitarity
• Universal description of dissipative Tomonaga-Luttinger liquids with SU($N$) spin symmetry: Exact spectrum and critical exponents
• Measuring entanglement entropy and its topological signature for phononic systems
• Real spectra in non-Hermitian topological insulators
• Non-Abelian generalization of non-Hermitian quasicrystal: PT-symmetry breaking, localization, entanglement and topological transitions
• Experimental observation of exceptional bound states in a classical circuit network
• Eigenstate entanglement entropy in $PT$ invariant non-Hermitian system
• Generalized bulk-boundary correspondence in periodically driven non-Hermitian systems
• Subregion Spectrum Form Factor via Pseudo Entropy
• Entanglement, non-Hermiticity, and duality
• Polarization and entanglement spectrum in non-hermitian systems
• Non-Hermitian dynamics and $\mathcal{P}\mathcal{T}$-symmetry breaking in interacting mesoscopic Rydberg platforms
• Non-Hermitian Topology in Hermitian Topological Matter
• Experimental observation of the Yang-Lee quantum criticality in open systems
• Modular Hamiltonian for (holographic) excited states
• Statistical mechanics for non-Hermitian quantum systems
• Non-normal Hamiltonian dynamics in quantum systems and its realization on quantum computers
• Weak Ergodicity Breaking in Non-Hermitian Many-body Systems
• Quantum criticality in interacting bosonic Kitaev-Hubbard models
• Real spectra, Anderson localization, and topological phases in one-dimensional quasireciprocal systems
• Characterizing the Bulk-Boundary Correspondence of one-dimensional non-Hermitian interacting systems by edge entanglement entropy
• Chiral metals and entrapped insulators in a one-dimensional topological non-Hermitian system
• Entanglement Hamiltonian in the non-Hermitian SSH model
• Real Non-Hermitian Energy Spectra Without Any Symmetry
• Infernal and Exceptional Edge Modes: Non-Hermitian Topology Beyond the Skin Effect
• Engineering Yang-Lee anyons via Majorana bound states
• Quantum walks of correlated photons in non-Hermitian photonic lattices
• Quantum entanglement and non-Hermiticity in free-fermion systems
• Dynamics of spectral correlations in the entanglement Hamiltonian of the Aubry-André-Harper model
• Many-body phase transitions in a non-Hermitian Ising chain
• Many-body entanglement and spectral clusters in the extended hard-core bosonic Hatano-Nelson model
• Entanglement phase transitions in non-Hermitian Floquet systems
• Physics of PT-Symmetric Quantum Systems at Finite Temperature
• Nontrivial worldline winding in non-Hermitian quantum systems
• Unravelling the edge spectra of non-Hermitian Chern insulators
• State-dependent Topological Invariants and Anomalous Bulk-Boundary Correspondence in non-Hermitian Topological Systems
• Imaginary gap-closed points and dynamics in a class of dissipative systems
• Quantum entanglement of fermionic symmetry-enriched quantum critical points in one dimension
• Quantum quenches in driven-dissipative quadratic fermionic systems with parity-time symmetry
• Thermodynamics and entanglement entropy of the non-Hermitian SSH model
• Detecting bulk and edge exceptional points in non-Hermitian systems through generalized Petermann factors
• Yang-Lee Zeros in Quantum Phase Transition: An Entanglement Perspective
• Entanglement Hamiltonian and effective temperature of non-Hermitian quantum spin ladders
• Skin Effect Induced Anomalous Dynamics from Charge-Fluctuating Initial States
• Unitarity of Symplectic Fermion in $\alpha$-vacua with Negative Central Charge
• Entangelment Entropy on Generalized Brillouin Zone
• Electric conductivity in non-Hermitian holography
• Anomalous hybridization of spectral winding topology in quantized steady-state responses
• Formal Green's function theory in non-Hermitian lattice systems
• Galois conjugates of String-net Model
• Non-Hermitian entanglement dip from scaling-induced exceptional criticality
• Nonlinear Hall effects with an exceptional ring
• Characterizing phase transitions and criticality in non-Hermitian extensions of the XY model
• Complex entanglement entropy for complex conformal field theory
• Berry curvature inside parity-time-symmetry protected exceptional surface
• Yang-Lee edge singularity and quantum criticality in non-Hermitian PXP model
• Work statistics and generalized Loschmidt echo for the Hatano-Nelson model
• Symmetries, Conservation Laws and Entanglement in Non-Hermitian Fermionic Lattices
• Quantum feedback induced entanglement relaxation and dynamical phase transition in monitored free fermion chains with Wannier-Stark ladder
• Breakdown of Linear Spin-Wave Theory in a Non-Hermitian Quantum Spin Chain
• Topologically protected negative entanglement
• Universal time evolution of string order parameter in quantum critical systems with boundary invertible or non-invertible symmetry breaking
• Topological extension including quantum jump
• Conformal symmetry in quasi-free Markovian open quantum systems
• Non-Hermitian Hopf insulators
• Characterizing the Yang-Lee zeros of the classical Ising model through dynamic quantum phase transitions
• Exceptional Points, Bulk-Boundary Correspondence, and Entanglement Properties for a Dimerized Hatano-Nelson Model with Staggered Potentials
• Fermionic Partial Transpose in the Overlap Matrix Framework for Entanglement Negativity
• Entanglement scaling behaviors of free fermions on hyperbolic lattices
• Path-integral Bosonization of $d=2$ PT symmetric models
• Entanglement manifestation of knot topology in a non-Hermitian lattice
• Quantum cluster kink and ring frustration
• Probing phase transitions in non-Hermitian systems with quantum entanglement
• Winding-control mechanism of non-Hermitian systems
• Generalised Entanglement Entropies from Unit-Invariant Singular Value Decomposition
• Asymptotic freedom, lost: Complex conformal field theory in the two-dimensional $O(N>2)$ nonlinear sigma model and its realization in Heisenberg spin chains
• Layer-number parity induced topological phase transition
• Fidelity and quantum geometry approach to Dirac exceptional points in diamond nitrogen-vacancy centers
• Non-Hermiticity induced thermal entanglement phase transition