Classification of topological phases in one dimensional interacting non-Hermitian systems and emergent unitarity

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.

15 pages, 5 figures

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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