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We show that the perturbation of the Su-Schrieffer-Heeger chain by alocalized lossy defect leads to higher-order exceptional points (HOEPs).Depending on the location of the defect, third- and fourth-order exceptionalpoints (EP3s & EP4s) appear in the space of Hamiltonian parameters. On the onehand, they arise due to the non-Abelian braiding properties of exceptionallines (ELs) in parameter space. Namely, the HOEPs lie at intersections ofmutually non-commuting ELs. On the other hand, we show that such specialintersections happen due to the fact that the delocalization of edge states,induced by the non-Hermitian defect, hybridizes them with defect states. Thesecan then coalesce together into an EP3. When the defect lies at the midpoint ofthe chain, a special symmetry of the full spectrum can lead to an EP4. In thisway, our model illustrates the emergence of interesting non-Abelian topologicalproperties in the multiband structure of non-Hermitian perturbations oftopological phases.

Braids and Higher-order Exceptional Points from the Interplay Between Lossy Defects and Topological Boundary States