Anomalous mechanisms of the loss of observability in non-Hermitian quantum models

Via several toy-model quantum Hamiltonians H (lambda) of a non-tridiagonal low-dimensional matrix form the existence of unusual observability horizons is revealed. At the corresponding limiting values of parameter lambda = lambda((critical)) these new types of quantum phase transitions are interpreted as the points of confluence of several decoupled Kato's exceptional points of equal or different orders. Such a phenomenon of degeneracy of non-Hermitian degeneracies seems to ask for a reclassification of the possible topologies of the complex energy Riemann surfaces in the vicinity of branch points. (C) 2020 The Author(s). Published by Elsevier B.V.