# Parallelized traveling cluster approximation to study numerically spin-fermion models on large lattices

## Abstract

Lattice spin-fermion models are quite important to study correlated systems where quantum dynamics allows for a separation between slow and fast degrees of freedom. The fast degrees of freedom are treated quantum mechanically while the slow variables, generically referred to as the “spins,” are treated classically. At present, exact diagonalization coupled with classical Monte Carlo (ED + MC) is extensively used to solve numerically a general class of lattice spin-fermion problems. In this common setup, the classical variables (spins) are treated via the standard MC method while the fermion problem is solved by exact diagonalization. The “traveling cluster approximation” (TCA) is a real space variant of the ED + MC method that allows to solve spin-fermion problems on lattice sizes with up to 10 ^{3} sites. In this paper, we present a novel reorganization of the TCA algorithm in a manner that can be efficiently parallelized. Finally, this allows us to solve generic spin-fermion models easily on 10 ^{4} lattice sites and with some effort on 10 ^{5} lattice sites, representing the record lattice sizes studied for this family of models.

- Authors:

- Univ. of Tennessee, Knoxville, TN (United States). Dept. of Physics and Astronomy
- Univ. of Tennessee, Knoxville, TN (United States). Dept. of Physics and Astronomy; Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Materials Science and Technology Division

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Univ. of Tennessee, Knoxville, TN (United States)

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

- OSTI Identifier:
- 1265560

- Alternate Identifier(s):
- OSTI ID: 1184707

- Grant/Contract Number:
- AC05-00OR22725; DMR-1404375

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print)

- Additional Journal Information:
- Journal Volume: 91; Journal Issue: 6; Journal ID: ISSN 1539-3755

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

### Citation Formats

```
Mukherjee, Anamitra, Patel, Niravkumar D., Bishop, Chris, and Dagotto, Elbio.
```*Parallelized traveling cluster approximation to study numerically spin-fermion models on large lattices*. United States: N. p., 2015.
Web. doi:10.1103/PhysRevE.91.063303.

```
Mukherjee, Anamitra, Patel, Niravkumar D., Bishop, Chris, & Dagotto, Elbio.
```*Parallelized traveling cluster approximation to study numerically spin-fermion models on large lattices*. United States. doi:10.1103/PhysRevE.91.063303.

```
Mukherjee, Anamitra, Patel, Niravkumar D., Bishop, Chris, and Dagotto, Elbio. Mon .
"Parallelized traveling cluster approximation to study numerically spin-fermion models on large lattices". United States. doi:10.1103/PhysRevE.91.063303. https://www.osti.gov/servlets/purl/1265560.
```

```
@article{osti_1265560,
```

title = {Parallelized traveling cluster approximation to study numerically spin-fermion models on large lattices},

author = {Mukherjee, Anamitra and Patel, Niravkumar D. and Bishop, Chris and Dagotto, Elbio},

abstractNote = {Lattice spin-fermion models are quite important to study correlated systems where quantum dynamics allows for a separation between slow and fast degrees of freedom. The fast degrees of freedom are treated quantum mechanically while the slow variables, generically referred to as the “spins,” are treated classically. At present, exact diagonalization coupled with classical Monte Carlo (ED + MC) is extensively used to solve numerically a general class of lattice spin-fermion problems. In this common setup, the classical variables (spins) are treated via the standard MC method while the fermion problem is solved by exact diagonalization. The “traveling cluster approximation” (TCA) is a real space variant of the ED + MC method that allows to solve spin-fermion problems on lattice sizes with up to 103 sites. In this paper, we present a novel reorganization of the TCA algorithm in a manner that can be efficiently parallelized. Finally, this allows us to solve generic spin-fermion models easily on 104 lattice sites and with some effort on 105 lattice sites, representing the record lattice sizes studied for this family of models.},

doi = {10.1103/PhysRevE.91.063303},

journal = {Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print)},

issn = {1539-3755},

number = 6,

volume = 91,

place = {United States},

year = {2015},

month = {6}

}

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