Path integral Monte Carlo with importance sampling for excitons interacting with an arbitrary phonon bath.

Area of Science:

• Quantum mechanics
• Condensed matter physics
• Computational chemistry

Background:

• Exciton dynamics are crucial in many physical and biological systems.
• Simulating exciton-phonon coupling at finite temperatures is computationally challenging.
• Accurate methods are needed to understand energy transfer and coherence.

Purpose of the Study:

• To develop and validate an efficient path integral Monte Carlo method for studying reduced density matrices of excitons coupled to phonon baths.
• To introduce a population-normalized estimator and an approximated gradient for improved computational performance.
• To demonstrate the method's applicability to model systems and complex environments.

Main Methods:

• Path integral Monte Carlo (PIMC) simulations.
• Development of a population-normalized estimator for the reduced density matrix.
• Application of the Metropolis-adjusted Langevin algorithm for importance sampling.
• Exploration of an approximated gradient for enhanced computational efficiency.

Main Results:

• An efficient and physically meaningful sampling function was obtained using the population-normalized estimator.
• Nonadiabatic phonon probability density was derived as a byproduct.
• The method accurately reproduced the temperature dependence of excitonic coherence and population in a model system.
• The developed sampling scheme is applicable to anharmonic environments and complex systems.

Conclusions:

• The developed path integral Monte Carlo method offers an efficient approach for simulating exciton-phonon dynamics.
• The population-normalized estimator and approximated gradient significantly improve computational scaling.
• This work provides a foundation for developing real-time propagation methods satisfying detailed balance conditions for exciton populations.