Hermitian--to--quasi-Hermitian quantum phase transitions

TL;DR

This paper explores quantum phase transitions where systems transition from Hermitian to quasi-Hermitian regimes, maintaining unitarity and observable energies, with insights illustrated through PT-symmetric examples.

Contribution

It analyzes the transition from Hermitian to quasi-Hermitian quantum systems, highlighting the behavior of observables and unitarity at the interface.

Findings

Quantum phase transition involves loss of Hermiticity, replaced by quasi-Hermiticity.

Unitarity and energy observability are preserved across the transition.

Elementary PT-symmetric models illustrate the transition features.

Abstract

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 ${\cal PT}-$symmetric examples.