# Correlation matrix renormalization theory for correlated-electron materials with application to the crystalline phases of atomic hydrogen

## Abstract

Developing accurate and computationally efficient methods to calculate the electronic structure and total energy of correlated-electron materials has been a very challenging task in condensed matter physics and materials science. Recently, we have developed a correlation matrix renormalization (CMR) method which does not assume any empirical Coulomb interaction U parameters and does not have double counting problems in the ground-state total energy calculation. The CMR method has been demonstrated to be accurate in describing both the bonding and bond breaking behaviors of molecules. In this study, we extend the CMR method to the treatment of electron correlations in periodic solid systems. By using a linear hydrogen chain as a benchmark system, we show that the results from the CMR method compare very well with those obtained recently by accurate quantum Monte Carlo (QMC) calculations. We also study the equation of states of three-dimensional crystalline phases of atomic hydrogen. We show that the results from the CMR method agree much better with the available QMC data in comparison with those from density functional theory and Hartree-Fock calculations.

- Authors:

- Ames Lab. and Iowa State Univ., Ames, IA (United States). Dept. of Physics and Astronomy
- Ames Lab. and Iowa State Univ., Ames, IA (United States). Dept. of Physics and Astronomy; Univ. of Virginia, Charlottesville, VA (United States). Dept. of Physics

- Publication Date:

- Research Org.:
- Ames Laboratory (AMES), Ames, IA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)

- OSTI Identifier:
- 1422467

- Alternate Identifier(s):
- OSTI ID: 1422456; OSTI ID: 1427729

- Report Number(s):
- IS-J-9602

Journal ID: ISSN 2469-9950; PRBMDO; TRN: US1801604

- Grant/Contract Number:
- AC02-07CH11358

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physical Review B

- Additional Journal Information:
- Journal Volume: 97; Journal Issue: 7; 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

```
Zhao, Xin, Liu, Jun, Yao, Yong-Xin, Wang, Cai-Zhuang, and Ho, Kai-Ming.
```*Correlation matrix renormalization theory for correlated-electron materials with application to the crystalline phases of atomic hydrogen*. United States: N. p., 2018.
Web. doi:10.1103/PhysRevB.97.075142.

```
Zhao, Xin, Liu, Jun, Yao, Yong-Xin, Wang, Cai-Zhuang, & Ho, Kai-Ming.
```*Correlation matrix renormalization theory for correlated-electron materials with application to the crystalline phases of atomic hydrogen*. United States. doi:10.1103/PhysRevB.97.075142.

```
Zhao, Xin, Liu, Jun, Yao, Yong-Xin, Wang, Cai-Zhuang, and Ho, Kai-Ming. Tue .
"Correlation matrix renormalization theory for correlated-electron materials with application to the crystalline phases of atomic hydrogen". United States.
doi:10.1103/PhysRevB.97.075142.
```

```
@article{osti_1422467,
```

title = {Correlation matrix renormalization theory for correlated-electron materials with application to the crystalline phases of atomic hydrogen},

author = {Zhao, Xin and Liu, Jun and Yao, Yong-Xin and Wang, Cai-Zhuang and Ho, Kai-Ming},

abstractNote = {Developing accurate and computationally efficient methods to calculate the electronic structure and total energy of correlated-electron materials has been a very challenging task in condensed matter physics and materials science. Recently, we have developed a correlation matrix renormalization (CMR) method which does not assume any empirical Coulomb interaction U parameters and does not have double counting problems in the ground-state total energy calculation. The CMR method has been demonstrated to be accurate in describing both the bonding and bond breaking behaviors of molecules. In this study, we extend the CMR method to the treatment of electron correlations in periodic solid systems. By using a linear hydrogen chain as a benchmark system, we show that the results from the CMR method compare very well with those obtained recently by accurate quantum Monte Carlo (QMC) calculations. We also study the equation of states of three-dimensional crystalline phases of atomic hydrogen. We show that the results from the CMR method agree much better with the available QMC data in comparison with those from density functional theory and Hartree-Fock calculations.},

doi = {10.1103/PhysRevB.97.075142},

journal = {Physical Review B},

number = 7,

volume = 97,

place = {United States},

year = {Tue Jan 23 00:00:00 EST 2018},

month = {Tue Jan 23 00:00:00 EST 2018}

}

Works referenced in this record:

##
Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set

journal, July 1996

- Kresse, G.; Furthmüller, J.
- Computational Materials Science, Vol. 6, Issue 1, p. 15-50

##
Efficient iterative schemes for *ab initio* total-energy calculations using a plane-wave basis set

journal, October 1996

- Kresse, G.; Furthmüller, J.
- Physical Review B, Vol. 54, Issue 16, p. 11169-11186