Researchers have discovered that even infinitesimal long-range interactions can dramatically reconfigure the spectrum and eigenstates of non-Hermitian quantum systems under open boundary conditions. This approximation, common in tight-binding models where long-range interactions are truncated, can fail dramatically in non-Hermitian systems. The mechanism is governed by a competition between the decay length of these interactions and the localization length of non-Hermitian skin modes, leading to a sharp transition as the decay rate is tuned.

The study details how, in one dimension, a "squeezed" generalized Brillouin zone (GBZ) replaces the original GBZ of the short-range Hamiltonian, reconstructing the open-boundary spectrum. For two or more dimensions, a "squeezed amoeba" formulation is proposed to describe the resulting spectral density. This finding is crucial because exponentially decaying long-range interactions are ubiquitous in realistic tight-binding models, and their truncation for model simplification can lead to erroneous descriptions of physical behavior.

The main implication is that these long-range interactions can qualitatively reshape the Green's function, a fundamental quantity in condensed matter physics that describes a system's response to a perturbation. This alteration of the Green's function, according to the authors, could be readily detected in experiments, opening the door for empirical verification of this phenomenon and a deeper understanding of non-Hermitian systems, which are relevant in fields such as optics and non-equilibrium quantum mechanics.