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This study compares ab initio thermal mean-field theories for fermions. Numerical and formal comparisons reveal differences between Fermi-Dirac, thermal Hartree-Fock, and perturbation theories, using full configuration interaction as a benchmark.

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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.