Non-Hermitian Bose-Hubbard-like quantum models

Abstract

Among all of the non-Hermitian large-tridiagonal-matrix quantum Hamiltonians we choose a subclass with the structure resembling the ``benchmark'' realistic Bose-Hubbard model. We demonstrate that this choice can be declared user-friendly in the sense that the underlying singular values can be specified via a ``Hermitized'' Schrödinger-like equation. In particular, the related ``Hermitized'' Green's functions is shown given the two alternative compact and numerically efficient matrix continued fraction forms.

talk presented to the XXIX Int. Conf. on Integrable Systems and Quantum Symmetries (Prague, CTU, July 7 - 11, 2025)

References in corpus (9)

• Making Sense of Non-Hermitian Hamiltonians
• Bose-Einstein Condensation in Magnetic Insulators
• A non-Hermitian $PT-$symmetric Bose-Hubbard model: eigenvalue rings from unfolding higher-order exceptional points
• Exact diagonalization: the Bose-Hubbard model as an example
• Generalized Bose-Hubbard Hamiltonians exhibiting a complete non-Hermitian degeneracy
• Bose-Einstein condensation processes with nontrivial geometric multiplicites realized via $\mathcal{P}\mathcal{T}-$symmetric and exactly solvable linear-Bose-Hubbard building blocks
• Complex tridiagonal quantum Hamiltonians and matrix continued fractions
• Few-grid-point simulations of Big Bang singularity in quantum cosmology
• Resonances and continued-fraction Green's functions in non-Hermitian Bose-Hubbard-like quantum models