Generalized Bose-Hubbard Hamiltonians exhibiting a complete non-Hermitian degeneracy

Abstract

The conventional toy-model constructions of phase diagrams often use various versions of the standard Hermitian Bose-Hubbard Hamiltonians $H$. These studies were recently extended to cover several non-Hermitian PT-symmetric versions of the model. A key technical merit of the extensions has been found in the existence of Kato's phase-transition-related exceptional-point spectral degeneracies of the $N$th order (EPN). In this setting, an ill-conditioned nature of $H$ near its EPN singularity represented a decisive technical obstacle. In our paper we show how the obstacle can be circumvented, leading to a broader class of the eligible models with tridiagonal and symmetric complex Hamiltonians $H^{(N)}(z)$ exhibiting the EPN degeneracies. The implementation of the method (requiring the use of computer-assisted symbolic manipulations at the larger integers $N$) is illustrated by sampling the real or complex spectra of energies near as well as far from the EPN dynamical regime.

arXiv comment22 pp., 7 figures

References in corpus (11)

• Making Sense of Non-Hermitian Hamiltonians
• Pseudo-Hermitian Representation of Quantum Mechanics
• Inverse design of third-order Dirac exceptional points in photonic crystals
• A non-Hermitian $PT-$symmetric Bose-Hubbard model: eigenvalue rings from unfolding higher-order exceptional points
• Signatures of three coalescing eigenfunctions
• Observation of Exceptional Points in Electronic Circuits
• Chirality of wave functions for three coalescing levels
• $\mathcal{P}\mathcal{T}$-symmetric wave guide system with evidence of a third-order exceptional point
• Optical Lattices with Higher-order Exceptional Points by Non-Hermitian Coupling
• Admissible perturbations and false instabilities in PT-symmetric quantum systems
• Complex symmetric Hamiltonians and exceptional points of order four and five

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• Quantum singularities in a solvable toy model
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• Resonances and continued-fraction Green's functions in non-Hermitian Bose-Hubbard-like quantum models
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