# Construction of non-PT-symmetric complex potentials with all-real spectra

## TL;DR

This paper reviews recent advances in constructing non-PT-symmetric complex potentials that possess entirely real spectra, expanding the understanding of spectral properties beyond traditional PT symmetry.

## Contribution

It introduces classes of non-PT-symmetric potentials with real spectra and discusses methods for their construction, including symmetry, supersymmetry, and soliton techniques.

## Key findings

- Existence of non-PT-symmetric potentials with all-real spectra
- Phase transitions without passing through exceptional points
- Generalization of PT symmetry to multi-dimensional systems

## Abstract

We review recent work on the generalization of PT symmetry. We show that, in addition to PT-symmetric complex potentials, there are also large classes of non-PT-symmetric complex potentials which also feature all-real spectra. In addition, some classes of these non-PT-symmetric potentials allow phase transitions which do or do not go through exceptional points. These non-PT-symmetric potentials are constructed by a variety of methods, such as the symmetry and supersymmetry methods and the soliton theory. A generalization of PT symmetry in multi-dimensions is also reviewed.