A Continued Fraction Resummation Form of Bath Relaxation Effect in the Spin-Boson Model

TL;DR

This paper introduces a continued fraction resummation method for the spin-boson model that systematically incorporates bath relaxation effects beyond second-order perturbation, improving quantum dynamics predictions.

Contribution

It develops a continued fraction form to resum high-order quantum kinetic expansion rate kernels, including an analytical sixth-order kernel, extending the Pade approximation.

Findings

Resummed approach extends Pade approximation.

Can fully recover exact quantum dynamics with higher orders.

Systematically accounts for bath relaxation effects.

Abstract

In the spin-boson model, a continued fraction form is proposed to systematically resum high-order quantum kinetic expansion (QKE) rate kernels, accounting for the bath relaxation effect beyond the second-order perturbation. In particular, the analytical expression of the sixth-order QKE rate kernel is derived for resummation. With higher-order correction terms systematically extracted from higher-order rate kernels, the resummed quantum kinetic expansion (RQKE) approach in the continued fraction form extends the Pade approximation and can fully recover the exact quantum dynamics as the expansion order increases.