Non-Hermitian CP-Symmetric Dirac Hamiltonians with Real Energy Eigenvalues

TL;DR

This paper introduces a broad class of non-Hermitian Dirac Hamiltonians that are invariant under a combined charge conjugation and parity symmetry, resulting in real energy spectra despite lacking PT-symmetry.

Contribution

It identifies and constructs non-Hermitian, non-PT-symmetric Dirac Hamiltonians with real spectra, expanding the understanding of symmetries ensuring real energies.

Findings

Hamiltonians exhibit real spectra despite non-Hermiticity.

Examples include systems with localized and continuum states.

Symmetry under charge conjugation and parity guarantees real energies.

Abstract

We present a large class of non-Hermitian non-PT-symmetric two-component Dirac Hamiltoninas with real energy spectra. These Hamiltonians are invariant under the combined action of "charge" conjugation (two-component transpose) and space-parity. Examples are given from the two subclasses of these systems having localized and/or continuum states with real energies.