On the eigenvalues of some non-Hermitian Hamiltonians with space-time   symmetry
  We calculate the eigenvalues of some two-dimensional non-Hermitian Hamiltonians by means of a pseudospectral method and straightforward diagonalization of the Hamiltonian matrix in a suitable basis set. Both sets of results agree remarkably well but differ considerably from the eigenvalues obtained some time ago by other authors. In particular, we do not observe the multiple phase transitions claimed to occur in one of the anharmonic oscillators. 
Paolo Amore, Francisco M. Fern\'andez, Javier Garcia
quant-ph