2026/08/03 by Mengjie Yang, Alexander N. Poddubny, Ching Hua Lee
Physics and Astronomy · Mathematics · #cond-mat.mes-hall #cond-mat.dis-nn #cond-mat.other #math-ph #math.MP #quant-ph
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arxiv created 2026/08/03 · arxiv updated 2026/08/05
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 Nc∼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, Nc∼ Dα/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 Nc/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.