Interplay of pseudo-Hermitian symmetries and degenerate manifolds in the eigenspectrum of non-Hermitian systems

In this letter, we study how the spectrum of pseudo-Hermitian systems is influenced by the ambiguity in the choice of the pseudo-metric operator. In particular, we analyze the case when different parameter-independent choices of pseudo-metric are possible and how it can lead to the appearance of robust degenerate manifolds in the parameter space of the system.