Topological invariants of complex energy plane in non-Hermitian systems
arXiv:2308.05329 · doi:10.1007/s11467-021-1122-5
Abstract
Non-Hermitian systems as theoretical models of open or dissipative systems exhibit rich novel physical properties and fundamental issues in condensed matter physics.We propose a generalized local-global correspondence between the pseudo-boundary states in the complex energy plane and topological invariants of quantum states. We find that the patterns of the pseudo-boundary states in the complex energy plane mapped to the Brillouin zone are topological invariants against the parameter deformation. We demonstrate this approach by the non-Hermitian Chern insulator model. We give the consistent topological phases obtained from the Chern number and vorticity. We also find some novel topological invariants embedded in the topological phases of the Chern insulator model, which enrich the phase diagram of the non-Hermitian Chern insulators model beyond that predicted by the Chern number and vorticity. We also propose a generalized vorticity and its flipping index to understand physics behind this novel local-global correspondence and discuss the relationships between the local-global correspondence and the Chern number as well as the transformation between the Brillouin zone and the complex energy plane. These novel approaches provide insights to how topological invariants may be obtained from local information as well as the global property of quantum states, which is expected to be applicable in more generic non-Hermitian systems.
arXiv comment27 pages, 6 figures, 46 conferences
References in corpus (34)
- Berry Phase Effects on Electronic Properties
- Edge states and topological invariants of non-Hermitian systems
- Topological phases of non-Hermitian systems
- Symmetry and Topology in Non-Hermitian Physics
- Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
- Topological Band Theory for Non-Hermitian Hamiltonians
- Anomalous edge state in a non-Hermitian lattice
- Non-Hermitian Chern bands
- Pseudo-Hermitian Representation of Quantum Mechanics
- Non-Hermitian robust edge states in one-dimension: Anomalous localization and eigenspace condensation at exceptional points
- Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
- Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
- Biorthogonal Quantum Mechanics
- Edge states and topological phases in non-Hermitian systems
- Second-Order Topological Phases in Non-Hermitian Systems
- Geometrical meaning of winding number and its characterization of topological phases in one-dimensional chiral non-Hermitian systems
- New topological invariants in non-Hermitian systems
- Topological states of non-Hermitian systems
- PT-Symmetry in Non-Hermitian Su-Schrieffer-Heeger model with complex boundary potentials
- Topological invariance and global Berry phase in non-Hermitian systems
- Topological Correspondence between Hermitian and Non-Hermitian Systems: Anomalous Dynamics
- Anomalous helical edge states in a non-Hermitian Chern insulator
- A theory of 2+1D bosonic topological orders
- Dynamical classification of topological quantum phases
- Topological invariants and phase diagrams for one-dimensional two-band non-Hermitian systems without chiral symmetry
- Hall Conductance of a Non-Hermitian Chern Insulator
- Topological invariants in dissipative extensions of the Su-Schrieffer-Heeger model
- Correlation Length, Universality Classes, and Scaling Laws Associated with Topological Phase Transitions
- Consistency of PT-symmetric quantum mechanics
- Universality classes of topological phase transitions with higher-order band crossing
- Finite-size effects in non-Hermitian topological systems
- Energy Observable for a Quantum System with a Dynamical Hilbert Space and a Global Geometric Extension of Quantum Theory
- Unification of topological invariants in Dirac models
- Quantization and Fractional Quantization of Currents in Periodically Driven Stochastic Systems I: Average Currents