RC-HEOM Hybrid Method for Non-Perturbative Open System Dynamics

TL;DR

The paper introduces RC-HEOM, a hybrid approach combining reaction-coordinate mapping with hierarchical equations of motion, enabling non-perturbative, non-Markovian analysis of open quantum systems with detailed bath information.

Contribution

It develops a novel hybrid method that unifies RC mapping and HEOM, allowing accurate, non-perturbative treatment of complex open quantum systems with accessible bath details.

Findings

Tracked the emergence of the Kondo singlet in Anderson impurity models.

Uncovered a nontrivial RC-mediated coherence revival.

Demonstrated the method's effectiveness in regimes challenging for traditional approaches.

Abstract

The Hierarchical equations of motion (HEOM) method is an important non-perturbative technique, allowing numerically exact treatment of open quantum systems with strong coupling and non-Markovian memory. However, its encoding of bath memory into auxiliary density operators often limits direct access to detailed bath information. In contrast, the reaction-coordinate (RC) mapping allows direct and transparent access to the dominant collective bath mode, but its perturbative and often Markovian treatment of the residual bath restricts its reliability. In this work, we introduce RC-HEOM, a hybrid method that unifies the strengths of both approaches by combining RC mapping with a fully non-perturbative HEOM description of the residual bath. RC-HEOM simultaneously retains exact non-Markovian memory and access to the RC mode, which enables analysis of system-RC information. Applying this method to the Anderson impurity models, we directly track the emergence of the Kondo singlet from the growth of the Kondo resonance and uncover a nontrivial RC-mediated coherence revival. These results demonstrate that RC-HEOM is a promising method for characterizing open quantum systems in regimes that are difficult to access with conventional master-equation methods.