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

## 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. Here we extract various exact free-energy correlation components and the exact adiabatic connection formula.

- Authors:

- Univ. of California, Irvine, CA (United States). Dept. of Physics and Astronomy
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Univ. of California, Berkeley, CA (United States). Dept. of Chemistry
- Univ. of California, Irvine, CA (United States). Dept. of Physics and Astronomy; Univ. of California, Irvine, CA (United States). Dept. of Chemistry

- Publication Date:

- Research Org.:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

- OSTI Identifier:
- 1389961

- Alternate Identifier(s):
- OSTI ID: 1257008

- Report Number(s):
- LLNL-JRNL-693045

Journal ID: ISSN 2469-9950; PRBMDO

- Grant/Contract Number:
- AC52-07NA27344; FG02-97ER25308; DGE-1321846; FG02-08ER46496

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physical Review B

- Additional Journal Information:
- Journal Volume: 93; Journal Issue: 24; Journal ID: ISSN 2469-9950

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

### Citation Formats

```
Smith, J. C., Pribram-Jones, A., and Burke, K..
```*Exact thermal density functional theory for a model system: Correlation components and accuracy of the zero-temperature exchange-correlation approximation*. United States: N. p., 2016.
Web. doi:10.1103/PhysRevB.93.245131.

```
Smith, J. C., Pribram-Jones, A., & Burke, K..
```*Exact thermal density functional theory for a model system: Correlation components and accuracy of the zero-temperature exchange-correlation approximation*. United States. doi:10.1103/PhysRevB.93.245131.

```
Smith, J. C., Pribram-Jones, A., and Burke, K.. Tue .
"Exact thermal density functional theory for a model system: Correlation components and accuracy of the zero-temperature exchange-correlation approximation". United States. doi:10.1103/PhysRevB.93.245131. https://www.osti.gov/servlets/purl/1389961.
```

```
@article{osti_1389961,
```

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

author = {Smith, J. C. and Pribram-Jones, A. and Burke, K.},

abstractNote = {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. Here we extract various exact free-energy correlation components and the exact adiabatic connection formula.},

doi = {10.1103/PhysRevB.93.245131},

journal = {Physical Review B},

number = 24,

volume = 93,

place = {United States},

year = {Tue Jun 14 00:00:00 EDT 2016},

month = {Tue Jun 14 00:00:00 EDT 2016}

}

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Works referenced in this record:

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Generalized Gradient Approximation Made Simple

journal, October 1996

- Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
- Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868

##
Self-Consistent Equations Including Exchange and Correlation Effects

journal, November 1965

- Kohn, W.; Sham, L. J.
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