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.

22 pp., 7 figures

References in corpus (3)

• Making Sense of Non-Hermitian Hamiltonians
• A non-Hermitian $PT-$symmetric Bose-Hubbard model: eigenvalue rings from unfolding higher-order exceptional points
• Chirality of wave functions for three coalescing levels

Cited by in corpus (5)

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• Resonances and continued-fraction Green's functions in non-Hermitian Bose-Hubbard-like quantum models
• Emergence and localization of exceptional points in an exactly solvable toy model
• Non-Hermitian Bose-Hubbard-like quantum models