dorsal/arxiv
View SchemaSpectral Topology and Delocalization in Disordered Hatano-Nelson Chains
| Authors | Supriyo Ghosh, Sergej Flach |
|---|---|
| Categories | |
| ArXiv ID | 2601.07236vv1 |
| URL | https://arxiv.org/abs/2601.07236 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
The unidirectional Hatano-Nelson chain serves as the fundamental non-Hermitian building block of the Su-Schrieffer-Heeger (SSH) model. We investigate its Anderson localization properties under diagonal binary disorder. For weak disorder, the complex eigenvalue spectrum forms a single closed loop, which bifurcates into two distinct loops at a critical disorder threshold. Correspondingly, the spectral winding number {\nu} undergoes a transition from {\nu} = 1 in the weak-disorder regime, through {\nu} = 1/2 at the critical point, to {\nu} = 0 in the strong-disorder limit. We show that the eigenstates are exponentially localized, with a localization length that varies analytically as a function of the loop parameter. Notably, at weak and critical disorder, the spectrum hosts two completely delocalized states with diverging localization lengths. This divergence is directly correlated with the non-trivial spectral winding number. These findings remain robust under various boundary conditions, with the exception of strictly open boundaries.
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"abstract": "The unidirectional Hatano-Nelson chain serves as the fundamental non-Hermitian building block of the Su-Schrieffer-Heeger (SSH) model. We investigate its Anderson localization properties under diagonal binary disorder. For weak disorder, the complex eigenvalue spectrum forms a single closed loop, which bifurcates into two distinct loops at a critical disorder threshold. Correspondingly, the spectral winding number {\\nu} undergoes a transition from {\\nu} = 1 in the weak-disorder regime, through {\\nu} = 1/2 at the critical point, to {\\nu} = 0 in the strong-disorder limit. We show that the eigenstates are exponentially localized, with a localization length that varies analytically as a function of the loop parameter. Notably, at weak and critical disorder, the spectrum hosts two completely delocalized states with diverging localization lengths. This divergence is directly correlated with the non-trivial spectral winding number. These findings remain robust under various boundary conditions, with the exception of strictly open boundaries.",
"arxiv_id": "2601.07236",
"authors": [
"Supriyo Ghosh",
"Sergej Flach"
],
"categories": [
"cond-mat.dis-nn"
],
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "Spectral Topology and Delocalization in Disordered Hatano-Nelson Chains",
"url": "https://arxiv.org/abs/2601.07236",
"version": "v1"
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