Critical parameters for non-hermitian Hamiltonians

PT-symmetric Hamiltonians exhibit real eigenvalues.Real eigenvalues appear when PT-symmetry is unbroken.The range of real eigenvalues is determined by exceptional points or critical parameters.The diagonalization method is suitable for the calculation of critical parameters.Degenerate eigenvalues require a more general definition of unbroken symmetry. We calculate accurate critical parameters for a class of non-hermitian Hamiltonians by means of the diagonalization method. We study three one-dimensional models and two perturbed rigid rotors with PT symmetry. One of the latter models illustrates the necessity of a more general condition for the appearance of real eigenvalues that we also discuss here.

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