A PT-Invariant Potential With Complex QES Eigenvalues
  We show that the quasi-exactly solvable eigenvalues of the Schr\"odinger equation for the PT-invariant potential $V(x) = -(\zeta \cosh 2x -iM)^2$ are complex conjugate pairs in case the parameter M is an even integer while they are real in case M is an odd integer. We also show that whereas the PT symmetry is spontaneously broken in the former case, it is unbroken in the latter case. 
Avinash Khare (IOP, Bhubaneswar) and Bhabani Prasad Mandal (SNBNCBS,   Calcutta)