Supersymmetry and the spontaneous breakdown of 𝒫𝒯 symmetry

Abstract
The appearances of complex eigenvalues in the spectra of -symmetric quantum mechanical systems are usually associated with a spontaneous breaking of . 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 -fold supersymmetry and quasi-exact solvability in certain special cases are pointed out.