How Long-Range Tails Reshape Non-Hermitian Spectra

• URL: http://arxiv.org/abs/2608.28577v1
• Date: Fri, 28 Aug 2026 17:53:36 GMT
• Title: How Long-Range Tails Reshape Non-Hermitian Spectra
• Abstract summary: We show that an infinitesimal long-range hopping can nonperturbatively reconstruct the spectrum and eigenstates of a short-range non-Hermitian system.<n>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.
• Score: 1.2702058978314932
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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