Symmetry-protected multifold exceptional points and their topological
characterization
- URL: http://arxiv.org/abs/2103.08232v2
- Date: Tue, 26 Oct 2021 15:32:16 GMT
- Title: Symmetry-protected multifold exceptional points and their topological
characterization
- Authors: Pierre Delplace, Tsuneya Yoshida and Yasuhiro Hatsugai
- Abstract summary: We investigate the existence of higher order exceptional points (EPs) in non-Hermitian systems.
We show that $mu$-fold EPs are stable in $mu-1$ dimensions in the presence of anti-unitary symmetries.
We 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.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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
$\pm1$. 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.
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