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Hauptverfasser: Zhong, Janet, Wang, Heming, Fan, Shanhui
Format: Preprint
Veröffentlicht: 2024
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Online-Zugang:https://arxiv.org/abs/2410.11257
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author Zhong, Janet
Wang, Heming
Fan, Shanhui
author_facet Zhong, Janet
Wang, Heming
Fan, Shanhui
contents There have been several criteria for the existence of topological edge states in 1D non-Hermitian two-band sublattice-symmetric tight-binding Hamiltonians. The generalized Brillouin zone (GBZ) approach uses the integration of the Berry connection over the GBZ contour in the complex wavevector space. An alternate `pole-zero' approach uses algebraic properties of the off-diagonal matrix elements of the sublattice-symmetric Hamiltonian in off-diagonal form. Both correctly predict the presence or absence of edge states, but there has not been an explicit proof of their equivalence. Here we provide such an explicit proof and moreover we extend the pole-zero approach so that it also applies for sublattice-symmetric models when the Hamiltonian is not in off-diagonal form. We give numerical examples for these invariants.
format Preprint
id arxiv_https___arxiv_org_abs_2410_11257
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Pole and zero edge state invariant for 1D non-Hermitian sublattice symmetry
Zhong, Janet
Wang, Heming
Fan, Shanhui
Mesoscale and Nanoscale Physics
Quantum Physics
There have been several criteria for the existence of topological edge states in 1D non-Hermitian two-band sublattice-symmetric tight-binding Hamiltonians. The generalized Brillouin zone (GBZ) approach uses the integration of the Berry connection over the GBZ contour in the complex wavevector space. An alternate `pole-zero' approach uses algebraic properties of the off-diagonal matrix elements of the sublattice-symmetric Hamiltonian in off-diagonal form. Both correctly predict the presence or absence of edge states, but there has not been an explicit proof of their equivalence. Here we provide such an explicit proof and moreover we extend the pole-zero approach so that it also applies for sublattice-symmetric models when the Hamiltonian is not in off-diagonal form. We give numerical examples for these invariants.
title Pole and zero edge state invariant for 1D non-Hermitian sublattice symmetry
topic Mesoscale and Nanoscale Physics
Quantum Physics
url https://arxiv.org/abs/2410.11257