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

It is known that the practical use of non-Hermitian (i.e., typically, image-symmetric) phenomenological quantum Hamiltonians image requires an efficient reconstruction of an ad hoc Hilbert-space metric image which would render the time-evolution unitary. Once one considers just the image-dimensional matrix toy models image, the matrix elements of image may be defined via a coupled set of image polynomial equations. Their solution is a typical task for computer-assisted symbolic manipulations. The feasibility of such a model-completion construction is illustrated here via a discrete square well model image endowed with a image-parametric close-to-the-boundary interaction image. The model is shown to possess (possibly, multiply degenerate) exceptional points marking the phase transitions which are attributable, due to the exact solvability of the model at any image, to the loss of the regularity of the metric. In the parameter-dependence of the energy spectrum near these singularities one encounters a broad variety of alternative, topologically non-equivalent scenarios.