Decays of degeneracies in PT-symmetric ring-shaped lattices

TL;DR

This paper investigates how spectral degeneracies in PT-symmetric ring-shaped lattices are lifted through perturbations, highlighting the effects of topology and non-Hermitian properties on their spectral behavior.

Contribution

It provides solvable models demonstrating the decay of degeneracies in PT-symmetric ring lattices due to perturbations, emphasizing the role of topology in spectral effects.

Findings

Spectral degeneracies are removed by perturbations at exceptional points.

Topology influences the spectral properties of PT-symmetric lattices.

Solvable examples illustrate the decay of degeneracies.

Abstract

Non-Hermitian ring-shaped discrete lattices share the appeal with their more popular linear predecessors. Their dynamics controlled by the nearest-neighbor interaction is equally phenomenologically interesting. In comparison, the innovative nontriviality of their topology may be expected to lead to new spectral effects. Some of them are studied here via solvable examples. Main attention is paid to the perturbation-caused removals of spectral degeneracy at exceptional points.