A new mechanism of quantum phase transitions proposed.
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The conventional one, via an isolated exceptional point (EP), generalized.
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The general horizon of a loss of observability interpreted as a confluence of EPs.
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Innovation illustrated via several non-Hermitian toy-model Hamiltonians.
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Constructions based on linear algebra kept non-numerical.
Abstract
Via several toy-model quantum Hamiltonians of a non-tridiagonal low-dimensional matrix form the existence of unusual observability horizons is revealed. At the corresponding limiting values of parameter 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.