Non-Hermitian robust edge states in one-dimension: Anomalous localization and eigenspace condensation at exceptional points

TL;DR

This paper explores non-Hermitian one-dimensional systems where a unique form of degeneracy, called a phenomenal point, leads to robust boundary states and localization phenomena, challenging traditional topological insulator concepts.

Contribution

It introduces the concept of phenomenal points in non-Hermitian lattices, revealing a new form of degeneracy that results in disorder-robust boundary states and localization.

Findings

Identification of phenomenal points with eigenspace condensation

Demonstration of disorder-robust boundary states in non-Hermitian systems

Observation of anomalous localization phenomena

Abstract

Capital to topological insulators, the bulk-boundary correspondence ties a topological invariant computed from the bulk (extended) states with those at the boundary, which are hence robust to disorder. Here we put forward an ordering unique to non-Hermitian lattices, whereby a pristine system becomes devoid of extended states, a property which turns out to be robust to disorder. This is enabled by a peculiar type of non-Hermitian degeneracy where a macroscopic fraction of the states coalesce at a single point with geometrical multiplicity of $1$, that we call a phenomenal point.