Exploiting the path-integral radius of gyration in open quantum dynamics

TL;DR

This paper introduces a novel approach to improve the efficiency of open quantum dynamics simulations by analyzing the path-integral radius of gyration and developing a pole-fitting algorithm for bath mode contributions.

Contribution

It demonstrates the equivalence of the Ishizaki--Tanimura correction to separating contributions to the radius of gyration and proposes an efficient pole-fitting method for low-temperature HEOM calculations.

Findings

Enhanced HEOM efficiency for fast baths

Effective pole-fitting of bath contributions

Improved low-temperature quantum dynamics simulations

Abstract

A major challenge in open quantum dynamics is the inclusion of Matsubara-decay terms in the memory kernel, which arise from the quantum-Boltzmann delocalisation of the bath modes. This delocalisation can be quantified by the radius of gyration squared ${\mathcal R}^2(\omega)$ of the imaginary-time Feynman paths of the bath modes as a function of the frequency $\omega$. In a Hierarchical Equations of Motion (HEOM) calculation with a Debye--Drude spectral density, ${\mathcal R}^2(\omega)$ is the only quantity that is treated approximately (assuming convergence with respect to hierarchy depth). Here, we show that the well-known Ishizaki--Tanimura correction is equivalent to separating smooth from `Brownian' contributions to ${\mathcal R}^2(\omega)$, and that modifying the correction leads to a more efficient HEOM in the case of fast baths. We also develop a simple `A4' adaptation of the `AAA' (Adaptive Antoulas--Anderson) algorithm in order to fit ${\mathcal R}^2(\omega)$ to a sum over poles, which results in an extremely efficient implementation of the standard HEOM method at low temperatures.