How Long-Range Tails Reshape Non-Hermitian Spectra

Abstract

Exponentially decaying long-range hoppings are ubiquitous in realistic tight-binding models and are often truncated to obtain a finite-range description. We show that this approximation can fail dramatically in non-Hermitian systems under open boundary conditions: an infinitesimal long-range hopping can nonperturbatively reconstruct the spectrum and eigenstates of a short-range non-Hermitian system. The mechanism is controlled by a competition between the decay length of infinitesimal long-range hoppings and the localization length of non-Hermitian skin modes, leading to a sharp transition as the decay rate is tuned. In one dimension, we show that a squeezed generalized Brillouin zone (GBZ) replaces the original GBZ of the short-ranged Hamiltonian, yielding the reconstructed open-boundary spectrum. In two or higher dimensions, we formulate a squeezed amoeba formulation describing the reconstructed spectral density. We further show that long-range hoppings can qualitatively reshape Green's function, which can be readily detected in experiments.

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BibTeX RIS

BibTeX

@misc{gu2026longrange,
  title = {{How Long-Range Tails Reshape Non-Hermitian Spectra}},
  author = {Ding Gu and Zhanpeng Fu and Yu-Min Hu and Zhong Wang},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.28577},
  eprint = {2608.28577},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.28577},
}

RIS

TY  - UNPB
TI  - How Long-Range Tails Reshape Non-Hermitian Spectra
AU  - Ding Gu
AU  - Zhanpeng Fu
AU  - Yu-Min Hu
AU  - Zhong Wang
PY  - 2026
DA  - 2026/08/28
PB  - arXiv
DO  - 10.48550/arxiv.2608.28577
UR  - https://arxiv.org/abs/2608.28577
AB  - Exponentially decaying long-range hoppings are ubiquitous in realistic tight-binding models and are often truncated to obtain a finite-range description. We show that this approximation can fail dramatically in non-Hermitian systems under open boundary conditions: an infinitesimal long-range hopping can nonperturbatively reconstruct the spectrum and eigenstates of a short-range non-Hermitian system. The mechanism is controlled by a competition between the decay length of infinitesimal long-range hoppings and the localization length of non-Hermitian skin modes, leading to a sharp transition as the decay rate is tuned. In one dimension, we show that a squeezed generalized Brillouin zone (GBZ) replaces the original GBZ of the short-ranged Hamiltonian, yielding the reconstructed open-boundary spectrum. In two or higher dimensions, we formulate a squeezed amoeba formulation describing the reconstructed spectral density. We further show that long-range hoppings can qualitatively reshape Green's function, which can be readily detected in experiments.
ER  -

Abstract

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