# 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…

## 6 Citations

Bulk-Boundary Correspondence for Non-Hermitian Hamiltonians via Green Functions.

- PhysicsPhysical review letters
- 2021

It is found that the non-Hermitian winding number in one dimension signals a topological phase transition in the bulk: It implies spatial growth of the bulk Green function.

Many-body topology of non-Hermitian systems

- Physics, MathematicsPhysical Review B
- 2022

Non-Hermiticity gives rise to unique topological phases that have no counterparts in Hermitian systems and are intrinsic to non-Hermitian systems. Such intrinsic non-Hermitian topological phases…

Topology and Quantized Response in Complex Spectral Evolution.

- Mathematics
- 2020

The spectral winding on the complex energy plane is a unique topology for non-Hermitian systems under the periodic boundary condition (PBC). Despite considerable efforts devoted to non-Hermitian…

Dynamic skin effects of non-Hermitian systems

- Physics
- 2022

We study the time evolution processes of non-Hermitian systems under the open boundary condition and conﬁrm that the dynamical skin eﬀect exists in non-Hermitian systems analytically, and unveil the…

Wave packet acceleration and inelastic scattering in non-Hermitian dynamics

- Physics
- 2022

We discover the mechanism of the formation the dynamic skin eﬀect in non-Hermitian dynamics, compare to the Hermitian counterpart, the Gaussian wave packet can be accelerated or decelerated during…

Exact formulas of the end-to-end Green's functions in non-Hermitian systems

- MathematicsPhysical Review B
- 2022

Green’s function in non-Hermitian systems has recently been revealed to be capable of directional amplification in some cases. The exact formulas for end-to-end Green’s functions are significantly…

## References

SHOWING 1-10 OF 12 REFERENCES

Why does bulk boundary correspondence fail in some non-hermitian topological models

- Physics
- 2017

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

- Physics, MathematicsThe European Physical Journal Special Topics
- 2018

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

- Physics
- 2009

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

- Physics, Mathematics
- 2013

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

- Physics
- 2017

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

- PhysicsNature
- 2015

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

- Physics
- 2013

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

- Physics
- 2018

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

- PhysicsNature Communications
- 2020

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

- Physics
- 2020

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…