# Exchange-correlation approximations for reduced-density-matrix-functional theory at finite temperature: Capturing magnetic phase transitions in the homogeneous electron gas

## Abstract

Here, we derive an intrinsically temperature-dependent approximation to the correlation grand potential for many-electron systems in thermodynamical equilibrium in the context of finite-temperature reduced-density-matrix-functional theory (FT-RDMFT). We demonstrate its accuracy by calculating the magnetic phase diagram of the homogeneous electron gas. We compare it to known limits from highly accurate quantum Monte Carlo calculations as well as to phase diagrams obtained within existing exchange-correlation approximations from density functional theory and zero-temperature RDMFT.

- Authors:

- Freie Univ. Berlin, Berlin (Germany); Max Planck Institute of Microstructure Physics, Halle (Germany)
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Max Planck Institute for the Structure and Dynamics of Matter, Hamburg (Germany)
- Max Planck Institute of Microstructure Physics, Halle (Germany)

- Publication Date:

- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1421860

- Alternate Identifier(s):
- OSTI ID: 1413812

- Report Number(s):
- SAND-2017-13495J

Journal ID: ISSN 2469-9926; PLRAAN; 659501; TRN: US1801577

- Grant/Contract Number:
- AC04-94AL85000; 200202; NA0003525

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physical Review A

- Additional Journal Information:
- Journal Volume: 96; Journal Issue: 6; Journal ID: ISSN 2469-9926

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Baldsiefen, Tim, Cangi, Attila, Eich, F. G., and Gross, E. K. U.
```*Exchange-correlation approximations for reduced-density-matrix-functional theory at finite temperature: Capturing magnetic phase transitions in the homogeneous electron gas*. United States: N. p., 2017.
Web. doi:10.1103/PhysRevA.96.062508.

```
Baldsiefen, Tim, Cangi, Attila, Eich, F. G., & Gross, E. K. U.
```*Exchange-correlation approximations for reduced-density-matrix-functional theory at finite temperature: Capturing magnetic phase transitions in the homogeneous electron gas*. United States. doi:10.1103/PhysRevA.96.062508.

```
Baldsiefen, Tim, Cangi, Attila, Eich, F. G., and Gross, E. K. U. Mon .
"Exchange-correlation approximations for reduced-density-matrix-functional theory at finite temperature: Capturing magnetic phase transitions in the homogeneous electron gas". United States.
doi:10.1103/PhysRevA.96.062508.
```

```
@article{osti_1421860,
```

title = {Exchange-correlation approximations for reduced-density-matrix-functional theory at finite temperature: Capturing magnetic phase transitions in the homogeneous electron gas},

author = {Baldsiefen, Tim and Cangi, Attila and Eich, F. G. and Gross, E. K. U.},

abstractNote = {Here, we derive an intrinsically temperature-dependent approximation to the correlation grand potential for many-electron systems in thermodynamical equilibrium in the context of finite-temperature reduced-density-matrix-functional theory (FT-RDMFT). We demonstrate its accuracy by calculating the magnetic phase diagram of the homogeneous electron gas. We compare it to known limits from highly accurate quantum Monte Carlo calculations as well as to phase diagrams obtained within existing exchange-correlation approximations from density functional theory and zero-temperature RDMFT.},

doi = {10.1103/PhysRevA.96.062508},

journal = {Physical Review A},

number = 6,

volume = 96,

place = {United States},

year = {Mon Dec 18 00:00:00 EST 2017},

month = {Mon Dec 18 00:00:00 EST 2017}

}

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Works referenced in this record:

##
Self-Consistent Equations Including Exchange and Correlation Effects

journal, November 1965

- Kohn, W.; Sham, L. J.
- Physical Review, Vol. 140, Issue 4A, p. A1133-A1138

##
Accurate and simple analytic representation of the electron-gas correlation energy

journal, June 1992

- Perdew, John P.; Wang, Yue
- Physical Review B, Vol. 45, Issue 23, p. 13244-13249