Non-Hermitian Bose-Hubbard-like quantum models

TL;DR

This paper introduces a subclass of non-Hermitian Bose-Hubbard-like models where the singular values can be efficiently computed using a Hermitized Schrödinger equation and matrix continued fractions, facilitating analysis of these complex systems.

Contribution

It presents a novel approach to analyze non-Hermitian Bose-Hubbard models by Hermitizing the problem, enabling easier computation of singular values and Green's functions.

Findings

Singular values can be specified via a Hermitized Schrödinger-like equation.

Green's functions can be efficiently computed using matrix continued fractions.

The approach simplifies the analysis of non-Hermitian Bose-Hubbard 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'' Schr\"{o}dinger-like equation. In particular, the related ``Hermitized'' Green's functions is shown given the two alternative compact and numerically efficient matrix continued fraction forms.