On stability issues of the HEOM method

Abstract

The Hierarchical Equations of Motion (HEOM) method has become one of the cornerstones in the simulation of open quantum systems and their dynamics. It is commonly referred to as a non-perturbative method. Yet, there are certain instances, where the necessary truncation of the hierarchy of auxiliary density operators seems to introduce errors which are not fully controllable. We investigate the nature and causes of this type of critical error both in the case of pure decoherence, where exact results are available for comparison, and in the spin-boson system, a full system-reservoir model. We find that truncating the hierarchy to any finite size can be problematic for strong coupling to a dissipative reservoir, in particular when combined with an appreciable reservoir memory time.

10 pags, 5 figures

References in corpus (9)

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• Managing Temperature in Open Quantum Systems Strongly Coupled with Structured Environments
• Dynamics of the Non-equilibrium spin Boson Model: A Benchmark of master equations and their validity
• Coupled Lindblad pseudomode theory for simulating open quantum systems
• Unifying methods for optimal control in non-Markovian quantum systems via process tensors
• Comparison between explicit and implicit discretization strategies for a dissipative thermal environment
• Purified pseudomode model for nonlinear system-bath interactions
• Testing bath correlation functions for open quantum dynamics simulations
• Markovian Embeddings of Non-Markovian Open System Dynamics