About the performance of perturbative treatments of the spin-boson dynamics within the hierarchical equations of motion approach

TL;DR

This paper evaluates the effectiveness of perturbative treatments within the hierarchical equations of motion framework for simulating spin-boson dynamics, especially under challenging conditions like sub-Ohmic spectra at zero temperature.

Contribution

It demonstrates how the extended FP-HEOM method can systematically analyze higher-order master equations and compares exact and approximate memory kernels in spin-boson models.

Findings

FP-HEOM effectively investigates higher-order master equations.

Performance of perturbative treatments varies with spectral distribution and temperature.

Comparison shows differences between exact FP-HEOM and NIBA memory kernels.

Abstract

The hierarchical equations of motion (HEOM) provide a numerically exact approach for simulating the dynamics of open quantum systems coupled to a harmonic bath. However, its applicability has traditionally been limited to specific spectral forms and relatively high temperatures. Recently, an extended version called Free-Pole HEOM (FP-HEOM) has been developed to overcome these limitations. In this study, we demonstrate that the FP-HEOM method can be systematically employed to investigate higher-order master equations by truncating the FP-HEOM hierarchy at a desired tier. We focus on the challenging scenario of the spin-boson problem with a sub-Ohmic spectral distribution at zero temperature and analyze the performance of the corresponding master equations. Furthermore, we compare the memory kernel for population dynamics obtained from the exact FP-HEOM dynamics with that of the approximate NIBA (Non-Interacting-Blip Approximation).