# Dynamical cluster approximation: Nonlocal dynamics of correlated electron systems

## Abstract

We recently introduced the dynamical cluster approximation (DCA), a technique that includes short-ranged dynamical correlations in addition to the local dynamics of the dynamical mean-field approximation while preserving causality. The technique is based on an iterative self-consistency scheme on a finite-size periodic cluster. The dynamical mean-field approximation (exact result) is obtained by taking the cluster to a single site (the thermodynamic limit). Here, we provide details of our method, explicitly show that it is causal, systematic, {phi} derivable, and that it becomes conserving as the cluster size increases. We demonstrate the DCA by applying it to a quantum Monte Carlo and exact enumeration study of the two-dimensional Falicov-Kimball model. The resulting spectral functions preserve causality, and the spectra and the charge-density-wave transition temperature converge quickly and systematically to the thermodynamic limit as the cluster size increases. (c) 2000 The American Physical Society.

- Authors:

- Department of Physics, University of Cincinnati, Cincinnati, Ohio 45221 (United States)
- (United States)
- (India)

- Publication Date:

- OSTI Identifier:
- 20216423

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. B, Condensed Matter and Materials Physics

- Additional Journal Information:
- Journal Volume: 61; Journal Issue: 19; Other Information: PBD: 15 May 2000; Journal ID: ISSN 1098-0121

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; CLUSTER MODEL; ELECTRONIC STRUCTURE; MEAN-FIELD THEORY; MONTE CARLO METHOD; CHARGE DENSITY; ELECTRON CORRELATION; METALS; HIGH-TC SUPERCONDUCTORS; THEORETICAL DATA

### Citation Formats

```
Hettler, M. H., Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, Mukherjee, M., Jarrell, M., Krishnamurthy, H. R., and Department of Physics, Indian Institute of Science, Bangalore 560012,.
```*Dynamical cluster approximation: Nonlocal dynamics of correlated electron systems*. United States: N. p., 2000.
Web. doi:10.1103/PhysRevB.61.12739.

```
Hettler, M. H., Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, Mukherjee, M., Jarrell, M., Krishnamurthy, H. R., & Department of Physics, Indian Institute of Science, Bangalore 560012,.
```*Dynamical cluster approximation: Nonlocal dynamics of correlated electron systems*. United States. doi:10.1103/PhysRevB.61.12739.

```
Hettler, M. H., Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, Mukherjee, M., Jarrell, M., Krishnamurthy, H. R., and Department of Physics, Indian Institute of Science, Bangalore 560012,. Mon .
"Dynamical cluster approximation: Nonlocal dynamics of correlated electron systems". United States. doi:10.1103/PhysRevB.61.12739.
```

```
@article{osti_20216423,
```

title = {Dynamical cluster approximation: Nonlocal dynamics of correlated electron systems},

author = {Hettler, M. H. and Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439 and Mukherjee, M. and Jarrell, M. and Krishnamurthy, H. R. and Department of Physics, Indian Institute of Science, Bangalore 560012,},

abstractNote = {We recently introduced the dynamical cluster approximation (DCA), a technique that includes short-ranged dynamical correlations in addition to the local dynamics of the dynamical mean-field approximation while preserving causality. The technique is based on an iterative self-consistency scheme on a finite-size periodic cluster. The dynamical mean-field approximation (exact result) is obtained by taking the cluster to a single site (the thermodynamic limit). Here, we provide details of our method, explicitly show that it is causal, systematic, {phi} derivable, and that it becomes conserving as the cluster size increases. We demonstrate the DCA by applying it to a quantum Monte Carlo and exact enumeration study of the two-dimensional Falicov-Kimball model. The resulting spectral functions preserve causality, and the spectra and the charge-density-wave transition temperature converge quickly and systematically to the thermodynamic limit as the cluster size increases. (c) 2000 The American Physical Society.},

doi = {10.1103/PhysRevB.61.12739},

journal = {Physical Review. B, Condensed Matter and Materials Physics},

issn = {1098-0121},

number = 19,

volume = 61,

place = {United States},

year = {2000},

month = {5}

}