The phenomenon of quantum phase transition is considered in the special case in which the evolution laws remain unitary and in which the bound-state energies remain observable. The conventional Hermiticity of observables is lost at the interface, replaced by the so-called quasi-Hermiticity. Several features of the passage of the system through the interface are discussed and illustrated by elementary illustrative $\mathcal{PT}$-symmetric examples.

• Received 10 October 2017
• Revised 10 March 2018

DOI:https://doi.org/10.1103/PhysRevA.97.042117