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.

Quantum Physics (quant-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Quantum Gases (cond-mat.quant-gas); Optics (physics.optics)

arXiv:2608.28577 [quant-ph]

(or arXiv:2608.28577v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.28577 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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