Nonlocality-induced critical-length hierarchy from non-Hermitian competition

• URL: http://arxiv.org/abs/2608.02746v1
• Date: Mon, 03 Aug 2026 18:00:18 GMT
• Title: Nonlocality-induced critical-length hierarchy from non-Hermitian competition
• Abstract summary: In short-range systems formed by two coupled chains, competition leads to the critical-length law $N_csimln D$.<n>Here we show that long-range hoppings fundamentally reorganizes this critical behavior, producing a hierarchy of distinct scaling laws.<n>Our results offer a platform-independent framework testable in programmable topoelectrical circuits, photonic lattices and digital quantum simulators.
• Score: 48.9823527611878
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Spectral transitions in non-Hermitian lattices often arise from the competition between non-reciprocal skin accumulation and inter-component hybridization. In short-range systems formed by two coupled chains, this competition conventionally leads to the logarithmic critical-length law $N_c\sim\ln D$, where $D$ is the transverse separation between the chains. Here we show that long-range hoppings fundamentally reorganizes this critical behavior, producing a hierarchy of distinct scaling laws. When only the hybridization couplings are power-law decaying with exponent $α$, the onset becomes algebraic, $N_c\sim D^{α/3}$. When the hoppings within each chain are themselves also power-law decaying, in addition to the hybridization couplings, the system enters a scale-covariant regime for $α<2$, in which the criticality threshold equation depends only on the system aspect ratio $N_c/D$. At $α=2$ and beyond, this regime is followed by a marginal logarithmically corrected and algebraically corrected regimes, respectively. We identify two new non-local mechanisms that enable this unconventional critical hierarchy: a nonanalytic band-edge dispersion from long-range intra-chain hoppings, and parity-mixing hybridization induced by non-reciprocity. Our results show that nonlocality systematically removes the physical length scales i.e. skin depth underlying conventional critical non-Hermitian skin behavior, offering a platform-independent framework testable in programmable topoelectrical circuits, photonic lattices and digital quantum simulators.

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