The horizons of observability in PT-symmetric four-site quantum lattices

TL;DR

This paper explores the observability limits in PT-symmetric four-site quantum lattices, analyzing the domain of admissible parameters and revealing complex coupling subdomains even in simple models.

Contribution

It provides a detailed analysis of the Hermitizability domain in PT-symmetric quantum graphs, highlighting the structure of parameter spaces in simple lattice models.

Findings

Weak- and strong-coupling subdomains are non-empty and disconnected.

The domain of admissible parameters has a complex, non-trivial structure.

Even simple systems exhibit rich parameter space topology.

Abstract

The "Hermitizability" problem of quantum theory is explained, discussed and illustrated via the discrete-lattice cryptohermitian quantum graphs. In detail, the description of the domain ${\cal D}$ of admissible parameters is provided for the "circular-model" three-parametric quantum Hamiltonian $H$ using periodic boundary conditions. It is emphasized that even in such an elementary system the weak- and strong-coupling subdomains of ${\cal D}$ become, unexpectedly, non-empty and disconnected.