Universal time-domain Prony fitting decomposition for optimized hierarchical quantum master equations.

Area of Science:

• Quantum chemistry
• Computational physics
• Theoretical chemistry

Background:

• Accurate modeling of quantum systems requires efficient methods for handling bath correlation functions.
• Hierarchical Equations of Motion (HEOM) formalism is powerful but computationally demanding, especially at low temperatures.
• Existing methods for spectral decomposition can be limited in applicability or efficiency.

Purpose of the Study:

• To develop and validate a novel, efficient time-domain method for exponential series decomposition.
• To improve the numerical efficiency of the HEOM formalism, enabling calculations in previously inaccessible regimes.
• To demonstrate the method's accuracy by comparing it with established techniques and applying it to a relevant physical model.

Main Methods:

• Development of the time-domain Prony fitting decomposition (t-PFD) algorithm.
• Application of t-PFD to arbitrary bath correlation functions.
• Calibration of t-PFD against the Padé spectrum decomposition method.
• Implementation of converged HEOM calculations using the t-PFD approach.

Main Results:

• t-PFD provides an accurate and efficient method for exponential series decomposition.
• Significant optimization of HEOM numerical efficiency, especially at low temperatures.
• Successful application and validation of t-PFD on the single-impurity Anderson model.

Conclusions:

• The proposed t-PFD method offers a significant advancement in computational quantum dynamics.
• t-PFD extends the applicability of HEOM to challenging low-temperature regimes.
• This method paves the way for more efficient and accurate simulations of complex quantum systems.