Braiding topology of symmetry-protected degeneracy points in non-Hermitian systems

TL;DR

This paper classifies symmetry-protected degeneracy points in non-Hermitian systems using algebraic topology, revealing complex merging behaviors and expanding understanding beyond traditional abelian models.

Contribution

It introduces a systematic topological classification for symmetry-protected degeneracy points and uncovers their non-abelian merging behavior in non-Hermitian systems.

Findings

Pairwise-created degeneracy points merge into higher-order points

Discovery of non-abelian merging behavior

Model and circuit simulations validate theoretical predictions

Abstract

Degeneracy points in non-Hermitian systems are of great interest. While a homotopic framework exists for understanding their behavior in the absence of symmetry, it does not apply to symmetry-protected degeneracy points with reduced codimension. In this work, utilizing algebraic topology, we provide a systematic classification of these symmetry-protected degenerate points and investigate the braid conservation rule followed by them. Using a model Hamiltonian and circuit simulation, we discover that, contrary to simple annihilation, pairwise-created symmetry-protected degeneracy points merge into a higher-order degeneracy point, which goes beyond the abelian picture. Our findings empower researchers across diverse fields to uncover new phenomena and applications harnessing symmetry-protected non-Hermitian degeneracy points.