Quantum anomaly, non-Hermitian skin effects, and entanglement entropy in open systems

Abstract

We investigate the roles of non-Hermitian topology in spectral properties and entanglement structures of open systems. In terms of spectral theory, we give a unified understanding of two interpretations of non-Hermitian topology: quantum anomaly and non-Hermitian skin effects, in which the bulk spectra extremely depend on the boundary conditions. In this context, the fact that the intrinsic higher-dimensional skin effects under the full open boundary condition need the presence of the topological defects is understood in terms of the anomalous fermion production such as the Rubakov-Callan effect in the presence of the magnetic monopole. In terms of the entanglement structure, we investigate steady states of fermionic open systems whose Liouvillian (rapidity) spectra host non-Hermitian topology. We analyze dissipation-driven Majorana steady states in zero-dimensional open systems and relate them to the Majorana edge modes of topological superconductors by using the entanglement entropy. We also analyze a steady state of a one-dimensional open Fermi system with a non-Hermitian topological spectrum and relate it to the chiral edge states of the Chern insulator on the basis of the trace index defined from the entanglement spectrum. These correspondences indicate that the entanglement generates circular nonreciprocal currents under the periodic boundary condition and the skin-effect voltage with fermion accumulation under the open boundary condition. Finally, we discuss several related topics such as pseudospectral behaviors of Liouvillian dynamics and skin effects in interacting systems.

arXiv comment18pages, 5 figures, classification table of skin effects is added

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• Non-Hermitian topological phenomena: A review
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• Entanglement Phase Transition Induced by the Non-Hermitian Skin Effect
• Many-body topology of non-Hermitian systems
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• Non-equilibrium stationary states of quantum non-Hermitian lattice models
• Two-dimensional non-Hermitian skin effect in an ultracold Fermi gas
• Non-Hermitian skin effect and self-acceleration
• Non-Hermitian skin clusters from strong interactions
• Exceptional Bound States and negative Entanglement Entropy
• Dislocation Non-Hermitian Skin Effect
• Enhancement of Second-Order Non-Hermitian Skin Effect by Magnetic Fields
• Topology by Dissipation: Majorana Bosons in Metastable Quadratic Markovian Dynamics
• Non-Hermitian Pseudo-Gaps
• Non-Hermitian skin effect beyond the tight-binding models
• Non-Hermitian band topology with generalized inversion symmetry
• Real space topological invariant and higher-order topological Anderson insulator in two-dimensional non-Hermitian systems
• Universal competitive spectral scaling from the critical non-Hermitian skin effect
• Quantum Criticality in Open Quantum Spin Chains with Nonreciprocity
• Quantum Entanglement of Non-Hermitian Quasicrystals
• Non-Hermitian Squeezed Polarons
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• Nonreciprocal Charge and Spin Transport Induced by Non-Hermitian Skin Effect in Mesoscopic Heterojunctions
• Quantum Simulation of the Bosonic Kitaev Chain
• Non-Hermitian topology in monitored quantum circuits
• Entanglement Spectrum Crossings Reveal non-Hermitian Dynamical Topology
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• Entanglement Entropy of Non-Hermitian Free Fermions
• Universal platform of point-gap topological phases from topological materials
• Measuring entanglement entropy and its topological signature for phononic systems
• Solvable non-Hermitian skin effect in many-body unitary dynamics
• Non-Abelian generalization of non-Hermitian quasicrystal: PT-symmetry breaking, localization, entanglement and topological transitions
• Anomalously large relaxation times in dissipative lattice models beyond the non-Hermitian skin effect
• Topological enhancement of non-normality in non-Hermitian skin effects
• Bridging the gap between topological non-Hermitian physics and open quantum systems
• Entanglement, non-Hermiticity, and duality
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• Engineering Dissipative Quasicrystals
• Topological zero modes and edge symmetries of metastable Markovian bosonic systems
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• Non-normal Hamiltonian dynamics in quantum systems and its realization on quantum computers
• Characterizing the Bulk-Boundary Correspondence of one-dimensional non-Hermitian interacting systems by edge entanglement entropy
• Filling up complex spectral regions through non-Hermitian disordered chains
• Kramers' degeneracy for open systems in thermal equilibrium
• Exploring the impact of fluctuation-induced criticality on non-hermitian skin effect and quantum sensors
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• Boundary-dependent dynamical instability of bosonic Green's function: Dissipative Bogoliubov-de Gennes Hamiltonian and its application to non-Hermitian skin effect
• Entangelment Entropy on Generalized Brillouin Zone
• Majorana zero-modes in a dissipative Rashba nanowire
• Topological directed amplification
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• Liouvillian skin effects in two-dimensional electron systems at finite temperatures
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