Exponentially growing bulk Green functions as signature of nontrivial non-Hermitian winding number in one dimension

@article{Zirnstein2020ExponentiallyGB,
  title={Exponentially growing bulk Green functions as signature of nontrivial non-Hermitian winding number in one dimension},
  author={Heinrich-Gregor Zirnstein and Bernd Rosenow},
  journal={arXiv: Mesoscale and Nanoscale Physics},
  year={2020}
}
A nonzero non-Hermitian winding number indicates that a gapped system is in a nontrivial topological class due to the non-Hermiticity of its Hamiltonian. While for Hermitian systems nontrivial topological quantum numbers are reflected by the existence of edge states, a nonzero non-Hermitian winding number impacts a system's bulk response. To establish this relation, we introduce the bulk Green function, which describes the response of a gapped system to an external perturbation on timescales… 

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References

SHOWING 1-10 OF 12 REFERENCES
Why does bulk boundary correspondence fail in some non-hermitian topological models
The bulk-boundary correspondence is crucial to topological insulators. It associates the existence of boundary states (with zero energy and possessing chiral or helical properties) with the
Topological states of non-Hermitian systems
Abstract Recently, the search for topological states of matter has turned to non-Hermitian systems, which exhibit a rich variety of unique properties without Hermitian counterparts. Lattices modeled
A non-Hermitian Hamilton operator and the physics of open quantum systems
The Hamiltonian Heff of an open quantum system consists formally of a first-order interaction term describing the closed (isolated) system with discrete states and a second-order term caused by the
Topological Invariants of Edge States for Periodic Two-Dimensional Models
Transfer matrix methods and intersection theory are used to calculate the bands of edge states for a wide class of periodic two-dimensional tight-binding models including a sublattice and spin degree
Parity-Time Symmetry meets Photonics: A New Twist in non-Hermitian Optics
In the past decade, the concept of parity-time symmetry, originally introduced in non-Hermitian extensions of quantum mechanical theories, has come into thinking of photonics, providing a fertile
Spawning rings of exceptional points out of Dirac cones
TLDR
The results indicate that the radiation existing in any open system can fundamentally alter its physical properties in ways previously expected only in the presence of material loss and gain.
Bulk-Edge Correspondence for Two-Dimensional Topological Insulators
Topological insulators can be characterized alternatively in terms of bulk or edge properties. We prove the equivalence between the two descriptions for two-dimensional solids in the single-particle
Non-Hermitian physics and PT symmetry
In recent years, notions drawn from non-Hermitian physics and parity–time (PT) symmetry have attracted considerable attention. In particular, the realization that the interplay between gain and loss
Topological framework for directional amplification in driven-dissipative cavity arrays
TLDR
A theoretical framework based on the introduction of a topological invariant that helps to understand non-reciprocity and directional amplification in driven-dissipative cavity arrays is presented.
Generalized bulk–boundary correspondence in non-Hermitian topolectrical circuits
The study of the laws of nature has traditionally been pursued in the limit of isolated systems, where energy is conserved. This is not always a valid approximation, however, as the inclusion of
...
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