Benchmarking the exponential ansatz for the Holstein model

Area of Science:

• Condensed Matter Physics
• Quantum Chemistry

Background:

• Polarons are fundamental quasiparticles arising from electron-phonon interactions.
• The single-electron Holstein model is a key theoretical framework for studying polaron behavior.

Purpose of the Study:

• To evaluate the effectiveness of the exponential ansatz for polaron ground-state wavefunctions.
• To compare different variants of the exponential ansatz within the Holstein model.
• To establish a benchmark for future polaron wavefunction development.

Main Methods:

• Investigated the exponential ansatz in coupled cluster, canonical transformation, and perturbative forms.
• Analyzed these methods across the parameter space of the Holstein model.
• Performed a benchmark study of wavefunction accuracy and efficiency.

Main Results:

• The exponential ansatz, in its various forms, demonstrates significant capability in describing polaron states.
• Performance variations were observed across different ansatz variants and model parameters.
• A comprehensive comparison provides insights into the strengths of each method.

Conclusions:

• The exponential ansatz is a powerful tool for studying single polaron physics.
• This benchmark guides the selection and development of advanced wavefunction methods for complex polaron systems.
• Future work can extend these findings to more sophisticated models beyond the single-electron Holstein model.