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The practical use of non-Hermitian (i.e., typically, PT-symmetric)phenomenological quantum Hamiltonians is discussed as requiring an explicitreconstruction of the {\em ad hoc} Hilbert-space metrics which would render thetime-evolution unitary. Just the N-dimensional matrix toy models Hamiltoniansare considered, therefore. For them, the matrix elements of alternative metricsare constructed via solution of a coupled set of polynomial equations, usingthe computer-assisted symbolic manipulations for the purpose. The feasibilityand some consequences of such a model-construction strategy are illustrated viaa discrete square well model endowed with multi-parametricclose-to-the-boundary real bidiagonal-matrix interaction. The degenerateexceptional points marking the phase transitions are then studied numerically.A way towards classification of their unfoldings in topologicallynon-equivalent dynamical scenarios is outlined.

annals of physics

Solvable model of quantum phase transitions and the  symbolic-manipulation-based study of its multiply degenerate exceptional  points and of their unfolding