Supersymmetry and the spontaneous breakdown of PT symmetry

TL;DR

This paper explores the relationship between PT symmetry breaking and supersymmetry breaking in quantum systems, revealing exact level crossings and connections to N-fold supersymmetry and quasi-exact solvability.

Contribution

It introduces models where PT symmetry breaking coincides with supersymmetry breaking, and links these phenomena to N-fold supersymmetry and quasi-exact solvability.

Findings

Exact level crossings identified in models.

PT symmetry breaking linked with supersymmetry breaking.

Connections to N-fold supersymmetry and quasi-exact solvability.

Abstract

The appearances of complex eigenvalues in the spectra of PT-symmetric quantum-mechanical systems are usually associated with a spontaneous breaking of PT. In this letter we discuss a family of models for which this phenomenon is also linked with an explicit breaking of supersymmetry. Exact level-crossings are located, and connections with N-fold supersymmetry and quasi-exact solvability in certain special cases are pointed out.