Essential implications of similarities in non-Hermitian systems

Abstract

In this paper, we show that three different generalized similarities enclose all unitary and anti-unitary symmetries that induce exceptional points in lower-dimensional non-Hermitian systems. We prove that the generalized similarity conditions result in a larger class of systems than any class defined by a unitary or anti-unitary symmetry. Further we highlight that the similarities enforce spectral symmetry on the Hamiltonian resulting in a reduction of the codimension of exceptional points. As a consequence we show that the similarities drive the emergence of exceptional points in lower dimensions without the more restrictive need for a unitary and/or anti-unitary symmetry.