Symmetry-protected exceptional and nodal points in non-Hermitian systems

TL;DR

This paper explores new types of degeneracies in non-Hermitian systems, including non-defective exceptional points and their relation to symmetries, expanding understanding of spectral features beyond traditional exceptional points.

Contribution

It introduces non-defective exceptional points and analyzes their symmetry protections, extending the classification of degeneracies in non-Hermitian systems.

Findings

Non-defective EPs are diagonalizable at these points.

Symmetries like PT, PPH, and pseudo-Hermitian protect EPs.

Ordinary nodal points can coexist with defective EPs when symmetries are broken.

Abstract

One of the unique features of non-Hermitian~(NH) systems is the appearance of non-Hermitian degeneracies known as exceptional points~(EPs). The extensively studied defective EPs occur when the Hamiltonian becomes non-diagonalizable. Aside from this degeneracy, we show that NH systems may host two further types of degeneracies, namely, non-defective EPs and ordinary (Hermitian) nodal points. The non-defective EPs manifest themselves by i) the diagonalizability of the NH Hamiltonian at these points, ii) the non-diagonalizability of the Hamiltonian along certain intersections of these points and iii) instabilities in the Jordan decomposition when approaching the points from certain directions. We demonstrate that certain discrete symmetries, namely parity-time, parity-particle-hole, and pseudo-Hermitian symmetry, guarantee the occurrence of both defective and non-defective EPs. We extend this list of symmetries by including the NH time-reversal symmetry in two-band systems. Two-band and four-band models exemplify our findings. Through an example, we further reveal that ordinary nodal points may coexist with defective EPs in NH models when the above symmetries are relaxed.