A simple improved low temperature correction for the hierarchical equations of motion

Area of Science:

• Quantum mechanics
• Physical chemistry
• Computational physics

Background:

• The Hierarchical Equations of Motion (HEOM) method provides exact quantum dynamics for systems coupled to harmonic baths.
• Standard HEOM requires numerous auxiliary operators for consistency with weak-coupling master equations, especially at low temperatures.

Purpose of the Study:

• To develop a novel low-temperature correction scheme for terminating the HEOM hierarchy.
• To restore consistency with the weak-coupling master equation using a minimal hierarchy.

Main Methods:

• A new low-temperature correction scheme based on Zwanzig projection is proposed.
• The scheme is applied to terminate the hierarchy in HEOM calculations.
• The method's performance is evaluated on various model systems, including the Fenna-Matthews-Olson complex.

Main Results:

• The proposed correction scheme alleviates the need for numerous auxiliary operators.
• Consistency with the weak-coupling master equation is achieved with a minimal hierarchy.
• Improved convergence of HEOM calculations is observed, extending beyond the weak-coupling limit.

Conclusions:

• The new closure scheme offers a more efficient and accurate approach to quantum dynamics simulations.
• The method is straightforward to implement in existing HEOM software.
• This advancement enhances the applicability of HEOM for studying complex quantum systems.