# Multigrid algorithm for staggered lattice fermions

## Abstract

Critical slowing down in Krylov methods for the Dirac operator presents a major obstacle to further advances in lattice field theory as it approaches the continuum solution. Here we formulate a multigrid algorithm for the Kogut-Susskind (or staggered) fermion discretization which has proven difficult relative to Wilson multigrid due to its first-order anti-Hermitian structure. The solution is to introduce a novel spectral transformation by the Kähler-Dirac spin structure prior to the Galerkin projection. We present numerical results for the two-dimensional, two-flavor Schwinger model; however, the general formalism is agnostic to dimension and is directly applicable to four-dimensional lattice QCD.

- Authors:

- Boston U.
- NVIDIA, Santa Clara
- Fermilab

- Publication Date:

- Research Org.:
- Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25); USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1457586

- Alternate Identifier(s):
- OSTI ID: 1437400

- Report Number(s):
- FERMILAB-PUB-18-073-CD; arXiv:1801.07823

1650136

- Grant/Contract Number:
- AC02-07CH11359; SC0015845

- Resource Type:
- Journal Article: Published Article

- Journal Name:
- Phys.Rev.

- Additional Journal Information:
- Journal Volume: D97; Journal Issue: 11

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Brower, Richard C., Clark, M. A., Strelchenko, Alexei, and Weinberg, Evan.
```*Multigrid algorithm for staggered lattice fermions*. United States: N. p., 2018.
Web. doi:10.1103/PhysRevD.97.114513.

```
Brower, Richard C., Clark, M. A., Strelchenko, Alexei, & Weinberg, Evan.
```*Multigrid algorithm for staggered lattice fermions*. United States. doi:10.1103/PhysRevD.97.114513.

```
Brower, Richard C., Clark, M. A., Strelchenko, Alexei, and Weinberg, Evan. Thu .
"Multigrid algorithm for staggered lattice fermions". United States.
doi:10.1103/PhysRevD.97.114513.
```

```
@article{osti_1457586,
```

title = {Multigrid algorithm for staggered lattice fermions},

author = {Brower, Richard C. and Clark, M. A. and Strelchenko, Alexei and Weinberg, Evan},

abstractNote = {Critical slowing down in Krylov methods for the Dirac operator presents a major obstacle to further advances in lattice field theory as it approaches the continuum solution. Here we formulate a multigrid algorithm for the Kogut-Susskind (or staggered) fermion discretization which has proven difficult relative to Wilson multigrid due to its first-order anti-Hermitian structure. The solution is to introduce a novel spectral transformation by the Kähler-Dirac spin structure prior to the Galerkin projection. We present numerical results for the two-dimensional, two-flavor Schwinger model; however, the general formalism is agnostic to dimension and is directly applicable to four-dimensional lattice QCD.},

doi = {10.1103/PhysRevD.97.114513},

journal = {Phys.Rev.},

number = 11,

volume = D97,

place = {United States},

year = {Thu Jun 28 00:00:00 EDT 2018},

month = {Thu Jun 28 00:00:00 EDT 2018}

}

Free Publicly Available Full Text

Publisher's Version of Record at 10.1103/PhysRevD.97.114513

Other availability

Save to My Library

You must Sign In or Create an Account in order to save documents to your library.