SciPost Physics

SciPost Phys. 7, 069 (2019) · published 28 November 2019

• doi: 10.21468/SciPostPhys.7.5.069
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Abstract

We study the properties of the entanglement spectrum in gapped non-interacting non-Hermitian systems, and its relation to the topological properties of the system Hamiltonian. Two different families of entanglement Hamiltonians can be defined in non-Hermitian systems, depending on whether we consider only right (or equivalently only left) eigenstates or a combination of both left and right eigenstates. We show that their entanglement spectra can still be computed efficiently, as in the Hermitian limit. We discuss how symmetries of the Hamiltonian map into symmetries of the entanglement spectrum depending on the choice of the many-body state. Through several examples in one and two dimensions, we show that the biorthogonal entanglement Hamiltonian directly inherits the topological properties of the Hamiltonian for line gapped phases, with characteristic singular and energy zero modes. The right (left) density matrix carries distinct information on the topological properties of the many-body right (left) eigenstates themselves. In purely point gapped phases, when the energy bands are not separable, the relation between the entanglement Hamiltonian and the system Hamiltonian breaks down.

• Denner et al., Infernal and exceptional edge modes: non-Hermitian topology beyond the skin effect
  J. Phys. Mater. 6, 045006 (2023) [Crossref]
• Zloshchastiev, Density Operator Approach to Turbulent Flows in Plasma and Atmospheric Fluids
  Universe 6, 216 (2020) [Crossref]
• Bergholtz et al., Exceptional topology of non-Hermitian systems
  Rev. Mod. Phys. 93, 015005 (2021) [Crossref]
• Chen et al., Quantum entanglement of non-Hermitian quasicrystals
  Phys. Rev. B 105, L121115 (2022) [Crossref]
• Arouca et al., Unconventional scaling at non-Hermitian critical points
  Phys. Rev. B 102, 245145 (2020) [Crossref]
• Doi et al., Pseudoentropy in dS/CFT and Timelike Entanglement Entropy
  Phys. Rev. Lett. 130, 031601 (2023) [Crossref]
• Sticlet et al.,
  3181, 030001 (2024) [Crossref]
• Shen et al., Non-Hermitian Fermi-Dirac Distribution in Persistent Current Transport
  Phys. Rev. Lett. 133, 086301 (2024) [Crossref]
• Mu et al., Emergent Fermi surface in a many-body non-Hermitian fermionic chain
  Phys. Rev. B 102, 081115 (2020) [Crossref]
• Sticlet et al., Kubo Formula for Non-Hermitian Systems and Tachyon Optical Conductivity
  Phys. Rev. Lett. 128, 016802 (2022) [Crossref]
• Yamamoto et al., Universal properties of dissipative Tomonaga-Luttinger liquids: Case study of a non-Hermitian XXZ spin chain
  Phys. Rev. B 105, 205125 (2022) [Crossref]
• Arouca et al., Mixed higher-order topology, and nodal and nodeless flat band topological phases in a superconducting multiorbital model
  Phys. Rev. B 110, 064520 (2024) [Crossref]
• Okuma et al., Quantum anomaly, non-Hermitian skin effects, and entanglement entropy in open systems
  Phys. Rev. B 103, 085428 (2021) [Crossref]
• Ortega-Taberner et al., From Hermitian critical to non-Hermitian point-gapped phases
  Phys. Rev. B 107, 235112 (2023) [Crossref]
• Wang et al., Ground object information extraction from hyperspectral remote sensing images using deep learning algorithm
  Microprocessors and Microsystems 87, 104394 104394 (2021) [Crossref]
• Dóra et al., Full counting statistics in the many-body Hatano-Nelson model
  Phys. Rev. B 106, 235125 (2022) [Crossref]
• Tang et al., Dynamical scaling of Loschmidt echo in non-Hermitian systems
  EPL 137, 40001 (2022) [Crossref]
• Li et al., Ground-state and thermal entanglements in non-Hermitian XY system with real and imaginary magnetic fields
  Quantum Inf Process 22, 277 (2023) [Crossref]
• Lu et al., Many-body entanglement and spectral clusters in the extended hard-core bosonic Hatano-Nelson model
  Phys. Rev. A 109, 042208 (2024) [Crossref]
• Guo et al., Singular topology of scattering matrices
  Phys. Rev. B 108, 155418 (2023) [Crossref]
• Tu et al., General properties of fidelity in non-Hermitian quantum systems with PT symmetry
  Quantum 7, 960 960 (2023) [Crossref]
• Miao et al., Crossover behavior at an exceptional point for quantum entanglement and correlation in a non-Hermitian XY spin system
  Phys. Rev. B 110, 014403 (2024) [Crossref]
• Dóra et al., Correlations at PT-Symmetric Quantum Critical Point
  Phys. Rev. Lett. 128, 146804 (2022) [Crossref]
• Banerjee et al., Non-Hermitian topological phases: principles and prospects
  J. Phys.: Condens. Matter 35, 333001 (2023) [Crossref]
• Chen et al., Weak ergodicity breaking in non-Hermitian many-body systems
  SciPost Phys. 15, 052 (2023) [Crossref]
• Guo et al., Composite quantum phases in non-Hermitian systems
  Phys. Rev. Research 5, 033181 (2023) [Crossref]
• Sun et al., Biorthogonal quantum criticality in non-Hermitian many-body systems
  Front. Phys. 17, 33502 (2022) [Crossref]
• Lieu et al., Kramers' degeneracy for open systems in thermal equilibrium
  Phys. Rev. B 105, L121104 (2022) [Crossref]
• Zou et al., Detecting bulk and edge exceptional points in non-Hermitian systems through generalized Petermann factors
  Front. Phys. 19, 23201 (2024) [Crossref]
• Meden et al., PT -symmetric, non-Hermitian quantum many-body physics—a methodological perspective
  Rep. Prog. Phys. 86, 124501 (2023) [Crossref]
• Itable et al., Entanglement entropy distinguishes PT-symmetry and topological phases in a class of non-unitary quantum walks
  Quantum Inf Process 22, 106 (2023) [Crossref]
• Tzeng et al., Hunting for the non-Hermitian exceptional points with fidelity susceptibility
  Phys. Rev. Research 3, 013015 (2021) [Crossref]
• Fossati et al., Symmetry-resolved entanglement in critical non-Hermitian systems
  Phys. Rev. B 107, 205153 (2023) [Crossref]
• Alsallom et al., Fate of the non-Hermitian skin effect in many-body fermionic systems
  Phys. Rev. Research 4, 033122 (2022) [Crossref]
• Lee et al., Unraveling non-Hermitian pumping: Emergent spectral singularities and anomalous responses
  Phys. Rev. B 102, 085151 (2020) [Crossref]
• Turkeshi et al., Entanglement and correlation spreading in non-Hermitian spin chains
  Phys. Rev. B 107, L020403 (2023) [Crossref]
• Du et al., Physics of PT -symmetric quantum systems at finite temperatures
  Phys. Rev. A 106, 032206 (2022) [Crossref]
• Kawabata et al., Many-body topology of non-Hermitian systems
  Phys. Rev. B 105, 165137 (2022) [Crossref]
• Kawabata et al., Non-Bloch band theory of non-Hermitian Hamiltonians in the symplectic class
  Phys. Rev. B 101, 195147 (2020) [Crossref]
• Wang et al., State-Dependent Topological Invariants and Anomalous Bulk-Boundary Correspondence in Non-Hermitian Topological Systems with Generalized Inversion Symmetry
  Chinese Phys. Lett. 37, 117303 (2020) [Crossref]
• Yokomizo et al., Topological semimetal phase with exceptional points in one-dimensional non-Hermitian systems
  Phys. Rev. Research 2, 043045 (2020) [Crossref]
• Cao et al., Statistical mechanics for non-Hermitian quantum systems
  Phys. Rev. Research 5, 033196 (2023) [Crossref]
• Wang et al., Berry phase and quantum entanglement in a nonreciprocal composite system
  Phys. Rev. A 109, 062220 (2024) [Crossref]
• Despres et al., Breakdown of linear spin-wave theory in a non-Hermitian quantum spin chain
  Phys. Rev. B 110, 094304 (2024) [Crossref]
• Pan et al., Point-gap topology with complete bulk-boundary correspondence and anomalous amplification in the Fock space of dissipative quantum systems
  Phys. Rev. B 103, 205425 (2021) [Crossref]
• Ma et al., Imaginary gap-closed points and dynamics in a class of dissipative systems
  Phys. Rev. B 109, 214311 (2024) [Crossref]
• McDonald et al., Nonequilibrium stationary states of quantum non-Hermitian lattice models
  Phys. Rev. B 105, 064302 (2022) [Crossref]
• Sarkar et al., Interplay of disorder and point-gap topology: Chiral modes, localization, and non-Hermitian Anderson skin effect in one dimension
  Phys. Rev. B 106, 014207 (2022) [Crossref]
• Kornich et al., Signature of PT -symmetric non-Hermitian superconductivity in angle-resolved photoelectron fluctuation spectroscopy
  Phys. Rev. Research 4, L022018 (2022) [Crossref]
• Modak et al., Eigenstate entanglement entropy in a PT -invariant non-Hermitian system
  Phys. Rev. A 103, 062416 (2021) [Crossref]
• Lee et al., Many-body approach to non-Hermitian physics in fermionic systems
  Phys. Rev. B 101, 121109 (2020) [Crossref]
• Bácsi et al., Dynamics of entanglement after exceptional quantum quench
  Phys. Rev. B 103, 085137 (2021) [Crossref]
• Dóra et al., Work statistics and generalized Loschmidt echo for the Hatano-Nelson model
  Phys. Rev. B 110, L121116 (2024) [Crossref]
• Kawabata et al., Higher-order non-Hermitian skin effect
  Phys. Rev. B 102, 205118 (2020) [Crossref]
• Chen et al., Characterizing bulk-boundary correspondence of one-dimensional non-Hermitian interacting systems by edge entanglement entropy
  Phys. Rev. B 105, 075126 (2022) [Crossref]
• Groenendijk et al., Universal Hall conductance scaling in non-Hermitian Chern insulators
  Phys. Rev. Research 3, 023001 (2021) [Crossref]
• Kawabata et al., Entanglement Phase Transition Induced by the Non-Hermitian Skin Effect
  Phys. Rev. X 13, 021007 (2023) [Crossref]
• Kawabata et al., Topological Field Theory of Non-Hermitian Systems
  Phys. Rev. Lett. 126, 216405 (2021) [Crossref]
• Ortega-Taberner et al., Polarization and entanglement spectrum in non-Hermitian systems
  Phys. Rev. B 105, 075103 (2022) [Crossref]
• Wang et al., Quantum criticality in interacting bosonic Kitaev-Hubbard models
  Phys. Rev. A 106, 053315 (2022) [Crossref]
• Lin et al., Topological non-Hermitian skin effect
  Front. Phys. 18, 53605 (2023) [Crossref]
• Qin et al., Universal competitive spectral scaling from the critical non-Hermitian skin effect
  Phys. Rev. B 107, 155430 (2023) [Crossref]
• Okuma et al., Topological Origin of Non-Hermitian Skin Effects
  Phys. Rev. Lett. 124, 086801 (2020) [Crossref]
• Chang et al., Entanglement spectrum and entropy in topological non-Hermitian systems and nonunitary conformal field theory
  Phys. Rev. Research 2, 033069 (2020) [Crossref]
• Kornich, Current-Voltage Characteristics of the Normal Metal-Insulator-PT-Symmetric Non-Hermitian Superconductor Junction as a Probe of Non-Hermitian Formalisms
  Phys. Rev. Lett. 131, 116001 (2023) [Crossref]
• Guo et al., Entanglement entropy of non-Hermitian free fermions
  J. Phys.: Condens. Matter 33, 475502 (2021) [Crossref]
• Zhou, Non-Abelian generalization of non-Hermitian quasicrystals: PT -symmetry breaking, localization, entanglement, and topological transitions
  Phys. Rev. B 108, 014202 (2023) [Crossref]
• Rottoli et al., Entanglement Hamiltonian in the non-Hermitian SSH model
  J. Stat. Mech. 2024, 063102 (2024) [Crossref]
• Lee, Exceptional Bound States and Negative Entanglement Entropy
  Phys. Rev. Lett. 128, 010402 (2022) [Crossref]
• Kawabata et al., Real spectra in non-Hermitian topological insulators
  Phys. Rev. Research 2, 033391 (2020) [Crossref]
• Wang et al., Berry curvature inside a PT -symmetry protected exceptional surface
  Phys. Rev. B 109, 115406 (2024) [Crossref]
• Sayyad et al., Entanglement spectrum crossings reveal non-Hermitian dynamical topology
  Phys. Rev. Research 3, 033022 (2021) [Crossref]
• Sticlet et al., Correlations at higher-order exceptional points in non-Hermitian models
  Phys. Rev. B 108, 075133 (2023) [Crossref]
• Nakamura et al., Bulk-Boundary Correspondence in Point-Gap Topological Phases
  Phys. Rev. Lett. 132, 136401 (2024) [Crossref]
• Sinha et al., Exceptional points and quantum phase transition in a fermionic extension of the Swanson oscillator
  Phys. Scr. 99, 105534 (2024) [Crossref]