Fig. 1: Scale-tailored localization (STL) in the unidirectional hopping model.
From: Scale-tailored localization and its observation in non-Hermitian electrical circuits
a Upper panel: Sketch of the lattice model with rolled boundary condition. Bottom panel: Different regimes (marked in different colors) of eigenstates’ localization with respect to the coupling strength δt. STL (inv. STL): the induced second-type eigenstates are localized on the left (right) boundary; Bloch: all second-type eigenstates are extended. b Eigenenergies for different combinations of (N, l) in the complex plane with δt = 0.1 (solid circles) or δt = 10 (empty diamonds). The cases of (N, l) = (40, 5), (40, 10), and (40, 20) are marked in red, purple, and pink, respectively. For reference, the black unit circle represents the spectra under periodic boundary conditions. c Spatial distributions of the second-type eigenstates for several typical values of δt with fixed (N, l) = (40, 20). d The perfect overlapping of rescaled spatial distributions by the coupling range l for different (N, l). e Rescaled spatial distributions by the total system size N with δt = 0.1 and l = 5.
