Symmetry indicator in non-Hermitian systems

TL;DR

This paper develops a framework for symmetry indicators in non-Hermitian systems by leveraging their relation to doubled Hermitianized Hamiltonians, enabling efficient topological phase diagnosis in these systems.

Contribution

It introduces a theory of symmetry indicators for non-Hermitian systems based on their mapping to Hermitianized Hamiltonians, extending classification tools to non-Hermitian topological phases.

Findings

Symmetry indicator groups for non-Hermitian systems are identified.

The approach links non-Hermitian symmetry indicators to those of Hermitian systems.

Explicit formulas for spinful electronic systems are provided.

Abstract

Recently, topological phases in non-Hermitian systems have attracted much attention because non-Hermiticity sometimes gives rise to unique phases with no Hermitian counterparts. Non-Hermitian Bloch Hamiltonians can always be mapped to doubled Hermitianized Hamiltonians with chiral symmetry, which enables us to utilize the existing framework for Hermitian systems into the classification of non-Hermitian topological phases. While this strategy succeeded in the topological classification of non-Hermitian Bloch Hamiltonians in the presence of internal symmetries, the generalization of symmetry indicators -- a way to efficiently diagnose topological phases -- to non-Hermitian systems is still elusive. In this work, we study a theory of symmetry indicators for non-Hermitian systems. We define space group symmetries of non-Hermitian Bloch Hamiltonians as ones of the doubled Hermitianized Hamiltonians. Consequently, symmetry indicator groups for chiral symmetric Hermitian systems are equivalent to those for non-Hermitian systems. Based on this equivalence, we list symmetry indicator groups for non-Hermitian systems in the presence of space group symmetries. We also discuss the physical implications of symmetry indicators for some symmetry classes. Furthermore, explicit formulas of symmetry indicators for spinful electronic systems are included in appendices.