Topological invariance and global Berry phase in non-Hermitian systems

Abstract

By studying the topological invariance andBerry phase in non-Hermitian systems, we reveal the basic properties of the complex Berry phase and generalize the global Berry phases Q to identify the topological invariance for non-Hermitian systems.We find thatQcan identify topological invariance in two kinds of non-Hermitian model, the two-level non-Hermitian Hamiltonian and the bipartite dissipative model. For the bipartite dissipative model, an abrupt change of the Berry phase in the parameter space reveals a quantum phase transition and is related to the exceptional points. These results give the basic relationships between the Berry phase and the quantum and topological phase transitions of non-Hermitian systems.

15 pages, 2 figures

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• Perspective: non-Hermitian physics in magnetic systems
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• Entanglement Spectrum Crossings Reveal non-Hermitian Dynamical Topology
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• Entanglement, non-Hermiticity, and duality
• Numerical calculation of the complex berry phase in non-Hermitian systems
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• Polarization and entanglement spectrum in non-hermitian systems
• Observation of a topological edge state stabilized by dissipation
• Kinked linear response from non-Hermitian cold-atom pumping
• Non-Hermitian non-Abelian topological insulators with $PT$ symmetry
• Complex Berry phase and imperfect non-Hermitian phase transitions
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• Topological phases of commensurate or incommensurate non-Hermitian Su-Schrieffer-Heeger lattices
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• Quantum entanglement and non-Hermiticity in free-fermion systems
• Identifying gap-closings in open non-Hermitian systems by Biorthogonal Polarization
• Anomalous dynamical response of non-Hermitian topological phases
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• Direct observation of energy band attraction effect in non-Hermitian systems
• Versatile Braiding of Non-Hermitian Topological Edge States
• Topological band theory of a generalized eigenvalue problem with Hermitian matrices: Symmetry-protected exceptional rings with emergent symmetry
• Non-Hermiticity stabilized Majorana zero modes in semiconductor-superconductor nanowires
• A symmetry-protected exceptional ring in a photonic crystal with negative index media
• Soft topological modes protected by symmetry in rigid mechanical metamaterials
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• Topological study of a Bogoliubov-de Gennes system of pseudo spin-$1/2$ bosons with conserved magnetization in a honeycomb lattice
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• Selection Rule for Topological Amplifiers in Bogoliubov de Gennes Systems
• Energy polarization and energy pumping in Rice-Mele chains
• Nonlinear Hall effects with an exceptional ring
• Analogue Hawking radiation as a tunneling in a two-level $\mathcal{P}\mathcal{T}$-symmetric system
• Topological Invariant for Multi-Band Non-hermitian Systems with Chiral Symmetry
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• Pseudo-Hermitian Topology of Multiband Non-Hermitian Systems
• Quantum geometrical effects in non-Hermitian systems
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• Hybrid Higher-Order Skin Topological Modes in the Two-Dimensional Su-Schrieffer-Heeger Model with Nonreciprocal Hoppings
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• Anti-parity-time topologically undefined state
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• Geometric criterion of topological phase transition for non-Hermitian systems
• Non-orientable Exceptional Points in Twisted Boundary Systems
• Interferometric Geometric Phases of $\mathcal{P}\mathcal{T}$-symmetric Quantum Mechanics