Phase Transitions in Quasi-Hermitian Quantum Models at Exceptional Points of Order Four

Abstract

Phase transition in quantum mechanics is interpreted as an evolution, at the end of which, typically, a parameter-dependent and Hermitizable Hamiltonian (Formula presented.) loses its observability. In the language of mathematics, such a “quantum catastrophe” occurs at an exceptional point of order N (EPN). Although the Hamiltonian (Formula presented.) itself becomes unphysical in the limit of (Formula presented.), it is shown that it can play the role of an unperturbed operator in an innovative perturbation-approximation analysis of the vicinity of the EPN singularity. As long as such an analysis is elementary at (Formula presented.) and purely numerical at (Formula presented.), we pick up (Formula presented.) and demonstrate that for an arbitrary quantum system, the specific (i.e., already sufficiently phenomenologically rich) EP4 degeneracy becomes accessible via a unitary evolution process. This process is shown realizable inside a parametric domain (Formula presented.), the boundaries of which are determined, near (Formula presented.), non-numerically. Possible relevance of such a mathematical result in the context of non-Hermitian photonics is emphasized. © 2026 by the author.