Many-body approach to non-Hermitian physics in fermionic systems

Abstract

In previous studies, the topological invariants of 1D non-Hermitian systems have been defined in open boundary condition (OBC) to satisfy the bulk-boundary correspondence. The extreme sensitivity of bulk energy spectra to boundary conditions has been attributed to the breakdown of the conventional bulk-boundary correspondence based on the topological invariants defined under periodic boundary condition (PBC). Here we propose non-Hermitian many-body polarization as a topological invariant for 1D non-Hermitian systems defined in PBC, which satisfies the bulk-boundary correspondence. Employing many-body methodology in the non-Hermitian Su-Schrieffer-Heeger model for fermions, we show the absence of non-Hermitian skin effect due to the Pauli exclusion principle and demonstrate the bulk-boundary correspondence using the invariant defined under PBC. Moreover, we show that the bulk topological invariant is quantized in the presence of chiral or generalized inversion symmetry. Our study suggests the existence of generalized crystalline symmetries in non-Hermitian systems, which give quantized topological invariants that capture the symmetry-protected topology of non-Hermitian systems.

arXiv comment6+3 pages, 4+3 figures

References in corpus (69)

• Topological Photonics
• Topological Photonics
• Making Sense of Non-Hermitian Hamiltonians
• Classification of topological quantum matter with symmetries
• Edge states and topological invariants of non-Hermitian systems
• Unidirectional Invisibility induced by PT-Symmetric Periodic Structures
• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• Topological phases of non-Hermitian systems
• The physics of exceptional points
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Topological Origin of Non-Hermitian Skin Effects
• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• Dynamically encircling exceptional points in a waveguide: asymmetric mode switching from the breakdown of adiabaticity
• Anomalous edge state in a non-Hermitian lattice
• Non-Bloch Band Theory of Non-Hermitian Systems
• Loss-induced suppression and revival of lasing
• Topological energy transfer in an optomechanical system with exceptional points
• Visualization of Branch Points in PT-Symmetric Waveguides
• Non-Hermitian Chern bands
• Non-Hermitian Boundary Modes
• Pseudo-Hermiticity versus PT-Symmetry II: A complete characterizatio n of non-Hermitian Hamiltonians with a real spectrum
• Anatomy of skin modes and topology in non-Hermitian systems
• Pseudo-Hermiticity versus PT-Symmetry III: Equivalence of pseudo-Her miticity and the presence of antilinear symmetries
• Observation of Bulk Fermi Arc and Polarization Half Charge from Paired Exceptional Points
• Non-Hermitian skin effect and chiral damping in open quantum systems
• Observation of non-Hermitian degeneracies in a chaotic exciton-polariton billiard
• Topology by Dissipation in Atomic Quantum Wires
• Biorthogonal Quantum Mechanics
• Pump-induced Exceptional Points in Lasers
• Introduction to PT-Symmetric Quantum Theory
• Hybrid higher-order skin-topological modes in non-reciprocal systems
• Non-Hermitian Topological Invariants in Real Space
• Entanglement spectrum of topological insulators and superconductors
• Topologically protected defect states in open photonic systems with non-hermitian charge-conjugation and parity-time symmetry
• Bulk-Boundary Correspondence in a Non-Hermitian System in One Dimension with Chiral-Inversion Symmetry
• The emergence, coalescence and topological properties of multiple exceptional points and their experimental realization
• Probing non-Hermitian Skin Effect and non-Bloch Phase Transitions
• Parity-time-symmetric quantum critical phenomena
• Topological states of non-Hermitian systems
• Non-Hermitian perspective of the band structure in heavy-fermion systems
• Exceptional rings in two-dimensional correlated systems with chiral symmetry
• Non-Hermitian extensions of higher-order topological phases and their biorthogonal bulk-boundary correspondence
• Symmetry-protected nodal phases in non-Hermitian systems
• Topological exceptional surfaces in non-Hermitian systems with parity-time and parity-particle-hole symmetries
• Information Retrieval and Criticality in Parity-Time-Symmetric Systems
• Non-Hermitian systems and topology: A transfer-matrix perspective
• Heralded magnetism in non-Hermitian atomic systems
• Topological Correspondence between Hermitian and Non-Hermitian Systems: Anomalous Dynamics
• Entanglement entropy and the Berry phase in solid states
• Exceptional Surfaces in PT-Symmetric Photonic Systems
• Non-Bloch topological invariants in a non-Hermitian domain-wall system
• Non-Hermitian Hopf-Link Exceptional Line Semimetals
• Bulk-boundary correspondence from the inter-cellular Zak phase
• Exceptional Links and Twisted Fermi Ribbons in non-Hermitian Systems
• Entanglement and spin squeezing in non-Hermitian phase transitions
• Topological edge states in the one-dimensional super-lattice Bose-Hubbard model
• Knotted Non-Hermitian Metals
• Experimental demonstration of an anisotropic exceptional point
• Non-Hermitian Topological Theory of Finite-Lifetime Quasiparticles: Prediction of Bulk Fermi Arc Due to Exceptional Point
• Generalized bulk-edge correspondence for non-hermitian topological systems
• Quantum Entanglement of Interacting Fermions in Monte Carlo
• Entanglement spectrum and symmetries in non-Hermitian fermionic non-interacting models
• Topological collective plasmons in bipartite chains of metallic nanoparticles
• Disorder-driven exceptional lines and Fermi ribbons in tilted nodal-line semimetals
• Geometric classification of non-Hermitian topological systems through the singularity ring
• Full-Counting Many-Particle Dynamics: Nonlocal and Chiral Propagation of Correlations
• Engineering tunable local loss in a synthetic lattice of momentum states
• Detecting edge degeneracy in interacting topological insulators through entanglement entropy
• Inversion symmetric non-Hermitian Chern insulator

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• Exceptional Topology of Non-Hermitian Systems
• Non-Hermitian Physics
• Non-Hermitian skin modes induced by on-site dissipations and chiral tunneling effect
• Entanglement Phase Transition Induced by the Non-Hermitian Skin Effect
• Winding Numbers and Generalized Mobility Edges in Non-Hermitian Systems
• Skin superfluid, topological Mott insulators, and asymmetric dynamics in interacting non-Hermitian Aubry-Andre-Harper models
• Unraveling non-Hermitian pumping: emergent spectral singularities and anomalous responses
• Many-body topology of non-Hermitian systems
• Non-Hermitian topological Mott insulators in one-dimensional fermionic superlattices
• Symmetry breaking and spectral structure of the interacting Hatano-Nelson model
• Non-Hermitian Many-Body Localization with Open Boundaries
• Non-Bloch band theory in bosonic Bogoliubov-de Gennes systems
• Fate of the non-Hermitian skin effect in many-body fermionic systems
• Non-Hermitian Topological Phases: Principles and Prospects
• Fate of fractional quantum Hall states in open quantum systems: characterization of correlated topological states for the full Liouvillian
• Non-Hermitian band topology with generalized inversion symmetry
• Biorthogonal quantum criticality in non-Hermitian many-body systems
• Untying links through anti-parity-time-symmetric coupling
• Machine learning topological invariants of non-Hermitian systems
• Many-Body Non-Hermitian Skin Effect for Multipoles
• Entanglement Entropy of Non-Hermitian Free Fermions
• Symmetry Indicators for Inversion-Symmetric Non-Hermitian Topological Band Structures
• Anatomy of open-boundary bulk in multiband non-Hermitian systems
• Eigenstate entanglement entropy in $PT$ invariant non-Hermitian system
• Non-Hermitian dynamics and $\mathcal{P}\mathcal{T}$-symmetry breaking in interacting mesoscopic Rydberg platforms
• Dynamical scaling of Loschmidt echo in non-Hermitian systems
• Polarization and entanglement spectrum in non-hermitian systems
• Green's functions of multiband non-Hermitian systems
• Effect of quantum jumps on non-Hermitian system
• Phase transitions and bunching of correlated particles in a non-Hermitian quasicrystal
• Full counting statistics in the many-body Hatano-Nelson model
• General criterion for non-Hermitian skin effects and Application: Fock space skin effects in many body systems
• Emergent Mott insulators and non-Hermitian conservation laws in an interacting bosonic chain with noninteger filling and nonreciprocal hopping
• Probing phase transitions in non-Hermitian systems with Multiple Quantum Coherences
• Steady-state edge burst: From free-particle systems to interaction-induced phenomena
• Characterizing the Bulk-Boundary Correspondence of one-dimensional non-Hermitian interacting systems by edge entanglement entropy
• Quantum criticality in interacting bosonic Kitaev-Hubbard models
• Emergent conservation in Floquet dynamics of integrable non-Hermitian models
• Chiral metals and entrapped insulators in a one-dimensional topological non-Hermitian system
• Topological properties of non-Hermitian Creutz Ladders
• Topological Transitions with an Imaginary Aubry-Andre-Harper Potential
• Many-body Non-Hermitian Skin Effect At Finite Temperatures
• Construction of Non-Hermitian Parent Hamiltonian from Matrix Product States
• Nontrivial worldline winding in non-Hermitian quantum systems
• Multifractality of many-body non-Hermitian skin effect
• Non-Hermitian Haldane-Hubbard model: Effective description of one- and two-body dissipation
• Non-Hermitian boost deformation
• Entanglement transitions in a periodically driven non-Hermitian Ising chain
• Non-Hermitian three-dimensional two-band Hopf insulator
• Relationship between the Electronic Polarization and the Winding Number in Non-Hermitian Systems
• Complex semiclassical theory for non-Hermitian quantum systems
• Electric polarization and its quantization in one-dimensional non-Hermitian chains
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• Dynamics in non-Hermitian systems with nonreciprocal coupling
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• Quantum quench dynamics in the Luttinger liquid phase of the Hatano-Nelson model
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• Electronic polarization in non-Bloch band theory
• Many-Body Non-Hermitian Skin Effect with Exact Steady States in the Dissipative Quantum Link Model
• Machine learning of mirror skin effects in the presence of disorder
• Skin effect and excitation spectral of interacting non-Hermitian system
• Work statistics and generalized Loschmidt echo for the Hatano-Nelson model
• Spin-Depairing-Induced Exceptional Fermionic Superfluidity
• Composite Quantum Phases in Non-Hermitian Systems
• Gain engineering and atom lasing in a topological edge state in synthetic dimensions
• Non-Hermitian Multipole Skin Effects Challenge Localization
• Topological phases of many-body non-Hermitian systems
• Bulk--Boundary Correspondence and Boundary Zero Modes in a Non-Hermitian Kitaev Chain Model
• Phase Diagram of a Non-Hermitian Chern Insulator: Destabilization of Chiral Edge States and Bulk-Boundary Correspondence
• Mixedness timescale in non-Hermitian quantum systems
• Topological spin textures in electronic non-Hermitian systems
• Non-Hermitian topological superconductivity with symmetry-enriched spectral and eigenstate features
• Interplay of non-Hermitian skin effect and electronic correlations in the non-Hermitian Hubbard model via Real-space dynamical mean field theory
• Engineering qubit dynamics in open systems with photonic synthetic lattices
• Winding-control mechanism of non-Hermitian systems
• Emergence of non-trivial phases in interacting non-Hermitian quasiperiodic chains with power-law hopping
• Survival of Hermitian Criticality in the Non-Hermitian Framework
• Floquet topological properties in the Non-Hermitian long-range system with complex hopping amplitudes