Symmetry-protected nodal phases in non-Hermitian systems

TL;DR

This paper explores how non-Hermitian symmetries influence the formation of exceptional points, revealing the emergence of stable nodal surfaces protected by symmetry in dissipative quantum systems.

Contribution

It demonstrates that non-Hermitian symmetries increase the dimension of exceptional point manifolds, leading to stable nodal surfaces in NH systems, supported by analytical models.

Findings

Exceptional points form higher-dimensional manifolds due to NH symmetries.

Nodal surfaces are stable if the protecting symmetry is preserved.

Models in 1D and 2D illustrate the generality of the results.

Abstract

Non-Hermitian (NH) Hamiltonians have become an important asset for the effective description of various physical systems that are subject to dissipation. Motivated by recent experimental progress on realizing the NH counterparts of gapless phases such as Weyl semimetals, here we investigate how NH symmetries affect the occurrence of exceptional points (EPs), that generalize the notion of nodal points in the spectrum beyond the Hermitian realm. Remarkably, we find that the dimension of the manifold of EPs is generically increased by one as compared to the case without symmetry. This leads to nodal surfaces formed by EPs that are stable as long as a protecting symmetry is preserved, and that are connected by open Fermi volumes. We illustrate our findings with analytically solvable two-band lattice models in one and two spatial dimensions, and show how they are readily generalized to generic NH crystalline systems.