On the real matrix representation of PT-symmetric operators

TL;DR

This paper examines how to construct real matrix representations of PT-symmetric operators, identifies limitations of existing methods, and proposes improvements to better handle non-Hermitian Hamiltonians with antiunitary symmetry.

Contribution

It reveals limitations of previous general recipes for real matrix representations and introduces a new approach to overcome these issues in PT-symmetric operators.

Findings

Existing methods have limitations for certain PT-symmetric operators

Proposed approach improves the construction of real matrix representations

Results align with earlier findings in specific cases

Abstract

We discuss the construction of real matrix representations of PT-symmetric operators. We show the limitation of a general recipe presented some time ago for non-Hermitian Hamiltonians with antiunitary symmetry and propose a way to overcome it. Our results agree with earlier ones for a particular case.