Multiply Degenerate Exceptional Points and Quantum Phase Transitions

Abstract

The realization of a genuine phase transition in quantum mechanics requires that at least one of the Kato's exceptional-point parameters becomes real. A new family of finite-dimensional and time-parametrized quantum-lattice models with such a property is proposed and studied. All of them exhibit, at a real exceptional-point time $t=0$, the Jordan-block spectral degeneracy structure of some of their observables sampled by Hamiltonian $H(t)$ and site-position $Q(t)$. The passes through the critical instant $t=0$ are interpreted as schematic simulations of non-equivalent versions of the Big-Bang-like quantum catastrophes.

17 pp., 7 figures

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Cited by in corpus (17)

• Perturbation Theory in the Complex Plane: Exceptional Points and Where to Find Them
• Unitarity corridors to exceptional points
• Admissible perturbations and false instabilities in PT-symmetric quantum systems
• Exceptional points near first- and second-order quantum phase transitions
• Passage through exceptional point: Case study
• Complex symmetric Hamiltonians and exceptional points of order four and five
• Two patterns of PT-symmetry breakdown in a non-numerical six-state simulation
• Confluences of exceptional points and a systematic classification of quantum catastrophes
• Bound states emerging from below the continuum in a solvable PT-symmetric discrete Schroedinger equation
• Broken Hermiticity phase transition in Bose-Hubbard model
• Quantization of Big Bang in crypto-Hermitian Heisenberg picture
• Bose-Einstein condensation processes with nontrivial geometric multiplicites realized via $\mathcal{P}\mathcal{T}-$symmetric and exactly solvable linear-Bose-Hubbard building blocks
• Hermitian--to--quasi-Hermitian quantum phase transitions
• Hermitian - non-Hermitian interfaces in quantum theory
• Arnold's potentials and quantum catastrophes II
• Few-grid-point simulations of Big Bang singularity in quantum cosmology
• Equations of motion governing the dynamics of the exceptional points of parameterically dependent nonhermitian Hamiltonians