Resonances and continued-fraction Green’s functions in non-Hermitian Bose–Hubbard-like quantum models

Abstract

With resonances treated as eigenstates of a non-Hermitian quantum Hamiltonian $H$, the task of localization of the complex energy eigenvalues of $H$ is considered. The paper is devoted to its reduced version in which one only computes the real quantities called singular values of $H$. It is shown that in such an approach (and under suitable constraints including the tridiagonality of $H$) the singular values can be sought as poles of a “Hermitized” Green’s function expressible in terms of a doublet of matrix continued fractions. A family of multi-bosonic Bose–Hubbard-like complex Hamiltonians is recalled for illustration purposes.