Classification of topological phases in one dimensional interacting non-Hermitian systems and emergent unitarity
arXiv:1911.01590 · doi:10.1016/j.scib.2021.04.027
Abstract
Topological phases in non-Hermitian systems have become fascinating subjects recently. In this paper, we attempt to classify topological phases in 1D interacting non-Hermitian systems. We begin with the non-Hermitian generalization of the Su-Schrieffer-Heeger (SSH) model and discuss its many-body topological Berry phase, which is well defined for all interacting quasi-Hermitian systems (non-Hermitian systems that have real energy spectrum). We then demonstrate that the classification of topological phases for quasi-Hermitian systems is exactly the same as their Hermitian counterparts. Finally, we construct the fixed point partition function for generic 1D interacting non-Hermitian local systems and find that the fixed point partition function still has a one-to-one correspondence to their Hermitian counterparts. Thus, we conclude that the classification of topological phases for generic 1D interacting non-Hermitian systems is still exactly the same as Hermitian systems.
arXiv comment15 pages, 5 figures
References in corpus (48)
- Edge states and topological invariants of non-Hermitian systems
- Topological phases of non-Hermitian systems
- Symmetry and Topology in Non-Hermitian Physics
- Symmetry protected topological orders and the group cohomology of their symmetry group
- Topological Band Theory for Non-Hermitian Hamiltonians
- Anomalous edge state in a non-Hermitian lattice
- Non-Bloch Band Theory of Non-Hermitian Systems
- Classification of Gapped Symmetric Phases in 1D Spin Systems
- Pseudo-Hermitian Representation of Quantum Mechanics
- Topological phases of fermions in one dimension
- Observation of non-Hermitian bulk-boundary correspondence in quantum dynamics
- Anatomy of skin modes and topology in non-Hermitian systems
- Classifying quantum phases using Matrix Product States and PEPS
- Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
- Probing topological invariants in the bulk of a non-Hermitian optical system
- Observation of Bulk Fermi Arc and Polarization Half Charge from Paired Exceptional Points
- Complex Edge-State Phase Transitions in 1D Topological Laser Arrays
- Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
- Second-Order Topological Phases in Non-Hermitian Systems
- Topological Transition in a Non-Hermitian Quantum Walk
- Topological phase transition in non-Hermitian quasicrystals
- Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
- Complete classification of 1D gapped quantum phases in interacting spin systems
- Bulk-Boundary Correspondence in a Non-Hermitian System in One Dimension with Chiral-Inversion Symmetry
- Higher-dimensional Algebra and Topological Quantum Field Theory
- Photonic Topological Insulating Phase Induced Solely by Gain and Loss
- A General Theorem Relating the Bulk Topological Number to Edge States in Two-dimensional Insulators
- Topological exceptional surfaces in non-Hermitian systems with parity-time and parity-particle-hole symmetries
- Defining a bulk-edge correspondence for non-Hermitian Hamiltonians via singular-value decomposition
- Non-Hermitian systems and topology: A transfer-matrix perspective
- Renormalization group transformations on quantum states
- Parity-time-symmetric topological superconductor
- Entanglement spectrum and entropy in topological non-Hermitian systems and non-unitary conformal field theories
- The Classification of Two-Dimensional Extended Topological Field Theories
- Interplay between long range hopping and disorder in topological systems
- Topological invariants and interacting one-dimensional fermionic systems
- Relation between -symmetry breaking and topologically nontrivial phases in the SSH and Kitaev models
- Hall Conductance of a Non-Hermitian Chern Insulator
- D-branes and K-theory in 2D topological field theory
- Non-Hermitian fractional quantum Hall states
- Lattice Topological Field Theory in Two Dimensions
- Multihole edge states in Su-Schrieffer-Heeger chains with interactions
- Excitation spectra and correlation functions of quantum Su-Schrieffer-Heeger models
- Topological bound states in interacting Su-Schrieffer-Heeger rings
- Phase structure of the interacting Su-Schrieffer-Heeger model and the relationship with the Gross-Neveu model on lattice
- Galois conjugated tensor fusion categories and non-unitary CFT
- Differentiable Cohomology of Gauge Groups
- Two-dimensional quantum walk with non-Hermitian skin effects
Cited by in corpus (25)
- Entanglement Phase Transition Induced by the Non-Hermitian Skin Effect
- 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
- Geometric Response and Disclination-Induced Skin Effects in Non-Hermitian Systems
- Non-Hermitian skin clusters from strong interactions
- Fate of the non-Hermitian skin effect in many-body fermionic systems
- Non-Hermitian Mott Skin Effect
- Non-Hermitian Floquet Topological Matter -- A Review
- Biorthogonal quantum criticality in non-Hermitian many-body systems
- Non-Hermitian Squeezed Polarons
- Reduction of one-dimensional non-Hermitian point-gap topology by correlations
- Entanglement, non-Hermiticity, and duality
- Symmetry-protected quantization of complex Berry phases in non-Hermitian many-body systems
- Quantum criticality in interacting bosonic Kitaev-Hubbard models
- Characterizing the Bulk-Boundary Correspondence of one-dimensional non-Hermitian interacting systems by edge entanglement entropy
- Correlation effects on non-Hermitian point-gap topology in zero dimension: reduction of topological classification
- A renormalization group approach to non-Hermitian topological quantum criticality
- Many-body phase transitions in a non-Hermitian Ising chain
- Multifractality of many-body non-Hermitian skin effect
- Non-Hermitian Haldane-Hubbard model: Effective description of one- and two-body dissipation
- Non-Hermitian three-dimensional two-band Hopf insulator
- Skin Effect Induced Anomalous Dynamics from Charge-Fluctuating Initial States
- Berry curvature inside parity-time-symmetry protected exceptional surface
- Composite Quantum Phases in Non-Hermitian Systems