Fermionic Statistics in the Strongly Correlated Limit of Density Functional Theory

Area of Science:

• Computational physics
• Quantum chemistry
• Condensed matter theory

Background:

• Kohn-Sham density functional theory (KS-DFT) is a powerful tool for electronic structure calculations.
• The exchange-correlation energy is a key component of KS-DFT, but its exact form is unknown.
• The adiabatic connection integrand, Wλ[ρ], provides a way to evaluate this energy.

Purpose of the Study:

• To verify theoretical predictions for the leading terms of Wλ[ρ] in the strong coupling limit (λ → ∞).
• To investigate the influence of fermionic statistics and spin effects on Wλ[ρ] at large coupling.
• To assess the asymptotic exactness of theoretical terms via numerical simulations.

Main Methods:

• Numerical implementation of the exact Levy functional for a two-electron system in one dimension.
• Theoretical analysis of the strong coupling limit (λ → ∞) of the adiabatic connection integrand.
• Investigation of spin effects within fermionic statistics at large coupling constants.

Main Results:

• The theoretical predictions for the two leading terms in the strong coupling limit were confirmed by numerical data.
• The asymptotic exactness of these leading terms was established for the model system.
• Fermionic statistics and spin effects were found to enter at orders of approximately e^(-√λ).

Conclusions:

• The leading terms in the strong coupling limit of the adiabatic connection integrand are asymptotically exact.
• This work provides the first study on the incorporation of spin effects in fermionic statistics at large coupling.
• The findings contribute to a more accurate evaluation of exchange-correlation energies in KS-DFT.