Universality and Dynamical Inequivalence in Isospectral Non-Hermitian Anderson Transitions

The Hatano Nelson paradigm establishes that extensive bulk nonreciprocity can destabilize Anderson localization via an imaginary gauge flux.

Here, we demonstrate that extensive nonreciprocity is not a necessary ingredient: a single non-Hermitian boundary bond in a disordered one-dimensional ring suffices to drive the localization-delocalization transition.

More generally, we construct an exactly isospectral family of non-Hermitian Hamiltonians that continuously interpolates between the uniform Hatano Nelson model and the single-bond limit.

We show that the universal critical behavior encompassing spectral, eigenstate, and topological diagnostics is gauge invariant and governed solely by the total imaginary gauge flux, regardless of its spatial distribution.

Remarkably, despite sharing identical spectra and critical exponents, different configurations within this isospectral family exhibit qualitatively distinct quantum dynamics, establishing a fundamental separation between static and dynamical universality in non-Hermitian systems.

Specifically, the single boundary realization features rapid operator scrambling, oscillatory wavepacket acceleration, and a double re-entrant steady state entanglement transition.

Finally, we propose an experimentally feasible realization based on multi-terminal topological transport, providing a realistic route toward observing boundary induced non Hermitian criticality and its unconventional dynamical signatures.