Solution of spin-boson systems in one and two-dimensional geometry via the asymptotic iteration method

TL;DR

This paper introduces an application of the asymptotic iteration method to solve spin-boson systems in one and two-dimensional geometries, providing a unified approach that reproduces known results and offers new insights.

Contribution

The paper develops a general matrix Hamiltonian framework and applies the asymptotic iteration method to solve it, extending previous methods to a broader class of physical models.

Findings

Reproduces earlier results in spin-boson systems

Provides a systematic solution approach for matrix Hamiltonians

Suggests potential generalizations of the method

Abstract

We consider solutions of the $2\times 2$ matrix Hamiltonian of physical systems within the context of the asymptotic iteration method. Our technique is based on transformation of the associated Hamiltonian in the form of the first order coupled differential equations. We construct a general matrix Hamiltonian which includes a wide class of physical models. The systematic study presented here reproduces a number of earlier results in a natural way as well as leading to new findings. Possible generalizations of the method are also suggested.