Technique for studying the coalescence of eigenstates and eigenvalues in non-Hermitian systems

Abstract

In our study, we explore high-order exceptional points (EPs), which are crucial for enhancing the sensitivity of open physical systems to external changes. We utilize the Hilbert−Schmidt speed (HSS), a measure of quantum statistical speed, to accurately identify EPs in non-Hermitian systems. These points are characterized by the simultaneous coalescence of eigenvalues and their associated eigenstates. One of the main benefits of using HSS is that it eliminates the need to diagonalize the evolved density matrix, simplifying the identification process. Our method is shown to be effective even in complex, multi-dimensional and interacting Hamiltonian systems. In certain cases, a generalized evolved state may be employed over the conventional normalized state. This necessitates the use of a metric operator to define the inner product between states, thereby introducing additional complexity. Our research confirms that HSS is a reliable and practical tool for detecting EPs, even in these demanding situations.

Graphical abstract

Keywords

non-Hermitian physics / exceptional points / Hilbert−Schmidt speed / quantum statistical speed

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Declarations

The authors declare that they have no competing interests and there are no conflicts.

Author contributions

All the authors conceived the work and agreed on the approach to pursue. H.R.J. planned and supervised the research in collaboration with M.A.-T. Moreover, S.M.H. and B.F. carried out the theoretical calculations, discussed the results and wrote the manuscript. The article was reviewed and edited by H.R.J. All authors gave final approval for publication.

Data availability statement

Data will be made available on reasonable request.

Additional information

Correspondence and requests for materials should be addressed to H.R.J.

Acknowledgements

M.A.-T. wishes to acknowledge the financial support of Urmia University (no grant number). H.R.J. acknowledges funding by grant number 1403 from Jahrom University.

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