Thermal mean-field theories

Area of Science:

• Quantum Many-Body Physics
• Computational Physics
• Theoretical Chemistry

Background:

• Accurate theoretical descriptions of fermion systems at finite temperatures are crucial for understanding various physical phenomena.
• Existing ab initio thermal mean-field theories offer different approximations with varying computational costs and accuracies.
• A systematic comparison is needed to evaluate their performance and identify suitable methods for specific applications.

Purpose of the Study:

• To compare several ab initio thermal mean-field theories for fermions.
• To analyze their formalisms and numerical predictions.
• To establish a benchmark for evaluating these theories.

Main Methods:

• Formal comparison of theoretical frameworks.
• Numerical evaluation of selected theories.
• Utilizing thermal full-configuration-interaction theory as a high-accuracy benchmark.
• Considering Fermi-Dirac theory, thermal Hartree-Fock (HF) theory, two modifications of the thermal single-determinant approximation, and first-order finite-temperature many-body perturbation theory.

Main Results:

• The study provides a detailed formalism-level comparison of the different theories.
• Numerical results highlight the quantitative differences in predictions among the compared methods.
• The benchmark calculations establish the accuracy of each theory relative to a highly accurate reference.

Conclusions:

• The comparison reveals the strengths and weaknesses of various ab initio thermal mean-field approaches.
• Understanding these differences is essential for selecting appropriate theoretical methods in fermionic system studies.
• This work contributes to the development and application of reliable computational methods in quantum many-body physics.