Discriminant indicators with generalized inversion symmetry

TL;DR

This paper introduces new discriminant indicators for systems with generalized inversion symmetry, enabling the detection of exceptional points from data at high-symmetry points, overcoming limitations of previous methods.

Contribution

It presents a novel approach to compute discriminant indicators solely from high-symmetry point data, improving robustness in identifying exceptional points in non-Hermitian systems.

Findings

Successfully analyzes 3x3 Hamiltonians with ambiguous reference energies

Indicators effectively detect symmetry-protected exceptional points

Method improves clarity over previous non-Hermitian discriminant indicators

Abstract

We propose indicators of the discriminant for systems with generalized inversion symmetry which are computed from data only at high-symmetry points in the Brillouin zone. Our approach captures the exceptional points and their symmetry-protected variants without ambiguity arising from the reference energy, which is advantage over the previously known indicators for non-Hermitian systems. As demonstrations, we systematically analyze $3\times 3$-Hamiltonians where the proper choice of the reference energy is not obvious.