Phase transitions in quasi-Hermitian quantum models at exceptional points of order four

Abstract

Quantum phase transition is interpreted as an evolution, at the end of which a parameter-dependent Hamiltonian $H(g)$ loses its observability. In the language of mathematics, such a quantum catastrophe occurs at an exceptional point of order $N$ (EPN). Although the Hamiltonian $H(g)$ itself becomes unphysical in the limit of $g\to g^{EPN}$, it is shown that it can play the role of an unperturbed operator in a perturbation-approximation analysis of the vicinity of the EPN singularity. Such an analysis is elementary at $N\le 3$ and numerical at $N\ge 5$, so we pick up $N=4$. We demonstrate that the specific EP4 degeneracy becomes accessible via a unitary evolution process realizable inside a parametric domain ${\mathcal{D}}_{\mathrm{physical}}$, the boundaries of which are determined non-numerically. Possible relevance of such a mathematical result in the context of non-Hermitian photonics is emphasized.

21 pp, 1 figure

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Cited by in corpus (1)

• Asymptotic non-Hermitian degeneracy phenomenon and its exactly solvable simulation