LETTER TO THE EDITOR: Supersymmetry and the spontaneous breakdown of P T symmetry

The appearances of complex eigenvalues in the spectra of P T-symmetric quantum mechanical systems are usually associated with a spontaneous breaking of P T. 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.