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

Abstract

Quantum phase transitions in certain non-Hermitian systems controlled by non-tridiagonal Hamiltonian matrices are found anomalous. In contrast to the known models with tridiagonal-matrix structure in which the geometric multiplicity of the completely degenerate energy eigenvalue appears always equal to one, this multiplicity is found larger than one in the present models. The phenomenon is interpreted as a confluence of several decoupled Kato's exceptional points of equal or different orders.

25 pages, 3 figures

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Cited by in corpus (7)

• Confluences of exceptional points and a systematic classification of quantum catastrophes
• Perturbation theory near degenerate exceptional points
• Exceptional points and domains of unitarity for a class of strongly non-Hermitian real-matrix Hamiltonians
• Paths of unitary access to exceptional points
• Bose-Einstein condensation processes with nontrivial geometric multiplicites realized via $\mathcal{P}\mathcal{T}-$symmetric and exactly solvable linear-Bose-Hubbard building blocks
• Quantum phase transitions mediated by clustered non-Hermitian degeneracies
• Swanson Hamiltonian: non-PT-symmetry phase