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Topological Quantum Computing Open Quantum Systems Decoherence Quantum Simulation

Non-Hermitian spectral flows and Berry-Chern monopoles

arXiv
Authors: Lucien Jezequel, Pierre Delplace

Year

2022

Paper ID

59492

Status

Preprint

Abstract Read

~2 min

Abstract Words

118

Citations

N/A

Abstract

We propose a non-Hermitian generalization of the correspondence between the spectral flow and the topological charges of band crossing points (Berry-Chern monopoles). A class of non-Hermitian Hamiltonians that display a complex-valued spectral flow is built by deforming an Hermitian model while preserving its analytical index. We relate those spectral flows to a generalized Chern number that we show to be equal to that of the Hermitian case, provided a line gap exists. We demonstrate the homotopic invariance of both the non-Hermitian Chern number and the spectral flow index, making explicit their topological nature. In the absence of a line gap, our system still displays a spectral flow whose topology can be captured by exploiting an emergent pseudo-Hermitian symmetry.

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  • We propose a non-Hermitian generalization of the correspondence between the spectral flow and the topological charges of band crossing points (Berry-Chern monopoles).

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2209.03876 [2] arXiv https://arxiv.org/abs/2209.03876 [3] Publisher https://arxiv.org/abs/2209.03876

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