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.

18pages, 5 figures, classification table of skin effects is added

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Cited by in corpus (51)

• Non-Hermitian topological phenomena: A review
• Topological Non-Hermitian skin effect
• Entanglement Phase Transition Induced by the Non-Hermitian Skin Effect
• Many-body topology of non-Hermitian systems
• Two-dimensional non-Hermitian skin effect in an ultracold Fermi gas
• Non-Hermitian skin effect and self-acceleration
• Dislocation Non-Hermitian Skin Effect
• Enhancement of Second-Order Non-Hermitian Skin Effect by Magnetic Fields
• 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
• Bulk-boundary correspondence in point-gap topological phases
• 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
• Non-Hermitian Maryland Model
• 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
• Anomalously large relaxation times in dissipative lattice models beyond the non-Hermitian skin effect
• Non-Abelian generalization of non-Hermitian quasicrystal: PT-symmetry breaking, localization, entanglement and topological transitions
• Topological enhancement of non-normality in non-Hermitian skin effects
• Polarization and entanglement spectrum in non-hermitian systems
• Engineering Dissipative Quasicrystals
• Topological zero modes and edge symmetries of metastable Markovian bosonic systems
• Phase transitions and bunching of correlated particles in a non-Hermitian quasicrystal
• Filling up complex spectral regions through non-Hermitian disordered chains
• Exploring the impact of fluctuation-induced criticality on non-hermitian skin effect and quantum sensors
• Phantom relaxation rate of the average purity evolution in random circuits due to Jordan non-Hermitian skin effect and magic sums
• Symmetric non-Hermitian skin effect with emergent nonlocal correspondence
• The Interplay of Finite and Infinite Size Stability in Quadratic Bosonic Lindbladians
• Simulating open quantum systems with giant atoms
• Imaginary gap-closed points and dynamics in a class of dissipative systems
• Protection of all nondefective twofold degeneracies by anti-unitary symmetries in non-Hermitian systems
• Investigation of a non-Hermitian edge burst with time-dependent perturbation theory
• Purity decay rate in random circuits with different configurations of gates
• 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
• Many-body Liouvillian dynamics with a non-Hermitian tensor-network kernel polynomial algorithm
• Topological directed amplification
• Dual Symmetry Classification of Non-Hermitian Systems and ${\mathbb{Z}}_2$ Point-Gap Topology of a Non-Unitary Quantum Walk
• Dissipation-driven topological phase transitions in open quantum systems independent of system Hamiltonian
• From Hermitian critical to non-Hermitian point-gapped phases
• Self-healing of non-Hermitian topological skin modes
• Liouvillian skin effects in two-dimensional electron systems at finite temperatures
• Floquet topological properties in the Non-Hermitian long-range system with complex hopping amplitudes
• Wiener-Hopf factorization and non-Hermitian topology for Amoeba formulation in one-dimensional multiband systems
• Boundary critical phenomena in the quantum Ashkin-Teller model
• Higher-order Liouvillian exceptional points in the dissipative dynamics of quadratic fermions