A preprint posted to arXiv — not yet peer-reviewed — argues that a standard modelling shortcut breaks down in a physically important class of quantum systems. When physicists simulate tight-binding lattices, they routinely truncate exponentially decaying long-range hoppings to keep the model finite-ranged. The authors claim this truncation can fail catastrophically in non-Hermitian systems under open boundary conditions: even an infinitesimally small long-range tail can nonperturbatively reconstruct the entire spectrum and eigenstates, rather than acting as a small perturbation.
The mechanism, according to the paper, turns on a competition between two length scales — the decay length of the residual long-range hopping and the localization length of non-Hermitian skin modes, which are eigenstates that pile up at system boundaries. When these lengths are comparable, the system crosses a sharp transition. In one dimension the authors describe the effect through a 'squeezed' generalized Brillouin zone that replaces the original one; in two or more dimensions they extend the analysis using what they call a squeezed amoeba formulation for the reconstructed spectral density. They further argue that the reshaping of the Green's function caused by long-range tails should be detectable experimentally.
If the analysis holds up under peer review, it would imply that widely used finite-range approximations demand more careful justification when applied to non-Hermitian Hamiltonians — a class that has attracted substantial interest for describing open quantum systems, photonic lattices, and systems with gain and loss. The result should be treated with appropriate caution until independent review is complete.