Imaginary-time hierarchical equations of motion for thermodynamic variables

Area of Science:

• Quantum thermodynamics
• Computational physics
• Condensed matter theory

Background:

• The partition function (PF) is crucial for quantum thermodynamics.
• The imaginary-time hierarchical equations of motion (imHEOM) method rigorously calculates the PF for systems coupled to non-Markovian baths.
• Evaluating the PF for complex quantum systems remains computationally challenging.

Purpose of the Study:

• To develop a numerically efficient scheme for evaluating the partition function (PF) using the imaginary-time hierarchical equations of motion (imHEOM) approach.
• To improve the computational efficiency of calculating quantum thermodynamic properties for strongly coupled systems.
• To present a novel method for handling non-Markovian bath interactions.

Main Methods:

• Utilizing β-differentiated imHEOM (BD-imHEOM) by differentiating imHEOM elements with respect to inverse temperature.
• Efficiently evaluating system, system-bath interaction, and heat-bath components of the PF.
• Employing polyharmonic decomposition for a concise hierarchical structure and improved convergence.

Main Results:

• The BD-imHEOM approach significantly enhances the numerical efficiency of PF calculations.
• The method allows for efficient computation of thermodynamic quantities for both system and bath components.
• Demonstrated successful application to spin-boson and spin lattice systems with Ohmic spectral distributions.

Conclusions:

• The BD-imHEOM scheme provides an efficient and accurate method for calculating quantum thermodynamic properties.
• The polyharmonic decomposition improves convergence and reduces computational cost.
• This approach offers a valuable tool for studying complex quantum systems interacting with non-Markovian environments.