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Essential implications of similarities in non-Hermitian systems

MPS-Authors

Montag,  Anton
Kunst Research Group, Marquardt Division, Max Planck Institute for the Science of Light, Max Planck Society;

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Kunst,  Flore K.
Kunst Research Group, Marquardt Division, Max Planck Institute for the Science of Light, Max Planck Society;

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2402.18249.pdf
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(Supplementary material), 23KB

Citation

Montag, A., & Kunst, F. K. (2024). Essential implications of similarities in non-Hermitian systems. arXiv, 2402.18249.


Cite as: https://hdl.handle.net/21.11116/0000-000E-8324-5
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.