Non-hermitian models in higher dimensions

TL;DR

This paper explores higher-dimensional non-hermitian models that can have real spectra without requiring explicit PT-symmetry or pseudo-hermiticity, broadening the understanding of spectral properties in such systems.

Contribution

It introduces a new class of higher-dimensional non-hermitian models where real spectra depend on coupling constants, extending previous frameworks.

Findings

Models can generate real spectra depending on coupling constants

Generalizes non-hermitian systems with real spectra beyond PT-symmetry

Expands the theoretical landscape of spectral properties in non-hermitian physics

Abstract

It is know that PT-symmetric models have real spectra provided the symmetry is not spontaneously broken. Even pseudo-hermitian models have real spectra, which enlarge the the class of non-hermitian models possessing real spectra. We however consider non-hermitian models in higher dimensions which are not necessarily explicit PT-symmetric nor pseudo-hermitian. We show that the models may generate real spectra depending upon the coupling constants of the Hamiltonian. Our models thus further generalize the class of non-hermitian systems, which possess real spectra.