Unitary unfoldings of Bose-Hubbard exceptional point with and without particle number conservation

Abstract

Non-Hermitian but $\mathcal{P}\mathcal{T}-$symmetric quantum system of an $N-$plet of bosons described by the three-parametric Bose-Hubbard Hamiltonian $H(\gamma ,v,c)$ is picked up, in its special exceptional-point limit $c\to 0$ and $\gamma \to v$, as an unperturbed part of the family of generalized Bose-Hubbard-like Hamiltonians $\mathfrak{H}(\lambda )=H(v,v,0)+\lambda \mathcal{V}$ for which the unitarity of the perturbed system is required. This leads to the construction of two different families of Hamiltonians $\mathfrak{H}(\lambda )$. In the first one the number $N$ of bosons is assumed conserved while in the second family such an assumption is relaxed. In both cases the anisotropy of the related physical Hilbert space is shown reflected by a highly counterintuitive but operationally realizable structure of admissible perturbations $\lambda \mathcal{V}$.

27 pp

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Cited by in corpus (3)

• Exceptional points and domains of unitarity for a class of strongly non-Hermitian real-matrix Hamiltonians
• Paths of unitary access to exceptional points
• Quantum phase transitions mediated by clustered non-Hermitian degeneracies