Symmetry-protected multifold exceptional points and their topological characterization

Abstract

We investigate the existence of higher order exceptional points (EPs) in non-Hermitian systems, and show that $\mu$-fold EPs are stable in $\mu -1$ dimensions in the presence of anti-unitary symmetries that are local in parameter space, such as e.g. PT or CP symmetries. This implies in particular that 3-fold and 4-fold symmetry-protected EPs are stable respectively in 2 and 3 dimensions. The stability of such exceptional points is expressed in terms of the homotopy properties of a "resultant vector" that we introduce. Our framework also allows us to rephrase the previously proposed ${\mathbb{Z}}_2$ index of PT and CP symmetric gapped phases beyond the realm of two-band models. We apply this general formalism to a frictional shallow water model that is found to exhibit 3-fold exceptional points associated with topological numbers $\pm 1$. For this model, we also show different non-Hermitian topological transitions associated with these exceptional points, such as their merging and a transition to a regime where propagation becomes forbidden.

accepted version to Phys. Rev. Lett

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