Universal Prony fitting decomposition for optimized hierarchical quantum master equations

TL;DR

This paper introduces a universal Prony fitting decomposition method that enhances the efficiency and accuracy of hierarchical quantum master equations, especially at low temperatures, by optimizing the HEOM formalism for complex bath correlation functions.

Contribution

The paper presents a novel Prony fitting decomposition technique that improves the hierarchical equations of motion for quantum systems, outperforming existing methods like Padé spectrum decomposition.

Findings

PFD accurately models arbitrary bath correlation functions.

Optimized HEOM formalism enables simulations at extremely low temperatures.

Demonstrated effectiveness on the single-impurity Anderson model.

Abstract

In this work, we propose the Prony fitting decomposition (PFD) as an accurate and efficient exponential series method, applicable to arbitrary interacting bath correlation functions. The resulting hierarchical equations of motion (HEOM) formalism is greatly optimized, especially in extremely low temperature regimes that would be inaccessible with other methods. For demonstration, we calibrate the present PFD against the celebrated Pad\'e spectrum decomposition method, followed by converged HEOM evaluations on the single-impurity Anderson model system.