Exact thermal density functional theory for a model system: Correlation components and accuracy of the zero-temperature exchange-correlation approximation

TL;DR

This paper provides exact calculations of thermal density functional theory components for a model system, assessing the accuracy of zero-temperature approximations at finite temperatures.

Contribution

It derives exact exchange-correlation free energy components and evaluates the zero-temperature approximation's accuracy using an exactly solvable Hubbard dimer model.

Findings

Zero-temperature approximation performs well at moderate temperatures and weak correlation.

Exact correlation components and adiabatic connection formula are obtained for the model.

The study offers benchmarks for thermal density functional theory methods.

Abstract

Thermal density functional theory calculations often use the Mermin-Kohn-Sham scheme, but employ ground-state approximations to the exchange-correlation (XC) free energy. In the simplest solvable nontrivial model, an asymmetric Hubbard dimer, we calculate the exact many-body energies and the exact Mermin-Kohn-Sham functionals for this system and extract the exact XC free energy. For moderate temperatures and weak correlation, we find this approximation to be excellent. We extract various exact free-energy correlation components and the exact adiabatic connection formula.