# NUMERICAL ALGORITHMS AT NON-ZERO CHEMICAL POTENTIAL. PROCEEDINGS OF RIKEN BNL RESEARCH CENTER WORKSHOP, VOLUME 19

## Abstract

The RIKEN BNL Research Center hosted its 19th workshop April 27th through May 1, 1999. The topic was Numerical Algorithms at Non-Zero Chemical Potential. QCD at a non-zero chemical potential (non-zero density) poses a long-standing unsolved challenge for lattice gauge theory. Indeed, it is the primary unresolved issue in the fundamental formulation of lattice gauge theory. The chemical potential renders conventional lattice actions complex, practically excluding the usual Monte Carlo techniques which rely on a positive definite measure for the partition function. This ''sign'' problem appears in a wide range of physical systems, ranging from strongly coupled electronic systems to QCD. The lack of a viable numerical technique at non-zero density is particularly acute since new exotic ''color superconducting'' phases of quark matter have recently been predicted in model calculations. A first principles confirmation of the phase diagram is desirable since experimental verification is not expected soon. At the workshop several proposals for new algorithms were made: cluster algorithms, direct simulation of Grassman variables, and a bosonization of the fermion determinant. All generated considerable discussion and seem worthy of continued investigation. Several interesting results using conventional algorithms were also presented: condensates in four fermion models, SU(2) gauge theory in fundamentalmore »

- Authors:

- Publication Date:

- Research Org.:
- Brookhaven National Lab., Upton, NY (US)

- Sponsoring Org.:
- RIKEN/BNL RESEARCH CENTER/DOE/ER (US)

- OSTI Identifier:
- 14643

- Report Number(s):
- BNL-52573; KB0201

R&D Project: PO03; KB0201; TRN: US0106196

- DOE Contract Number:
- AC02-98CH10886

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: PBD: 14 Sep 1999

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ALGORITHMS; BOSON EXPANSION; CONDENSATES; FERMIONS; PARTITION FUNCTIONS; PHASE DIAGRAMS; QUANTUM CHROMODYNAMICS; QUARK MATTER; QUARKS; COMPUTERIZED SIMULATION; VERIFICATION; LATTICE FIELD THEORY

### Citation Formats

```
BLUM,T.
```*NUMERICAL ALGORITHMS AT NON-ZERO CHEMICAL POTENTIAL. PROCEEDINGS OF RIKEN BNL RESEARCH CENTER WORKSHOP, VOLUME 19*. United States: N. p., 1999.
Web. doi:10.2172/14643.

```
BLUM,T.
```*NUMERICAL ALGORITHMS AT NON-ZERO CHEMICAL POTENTIAL. PROCEEDINGS OF RIKEN BNL RESEARCH CENTER WORKSHOP, VOLUME 19*. United States. doi:10.2172/14643.

```
BLUM,T. Tue .
"NUMERICAL ALGORITHMS AT NON-ZERO CHEMICAL POTENTIAL. PROCEEDINGS OF RIKEN BNL RESEARCH CENTER WORKSHOP, VOLUME 19". United States. doi:10.2172/14643. https://www.osti.gov/servlets/purl/14643.
```

```
@article{osti_14643,
```

title = {NUMERICAL ALGORITHMS AT NON-ZERO CHEMICAL POTENTIAL. PROCEEDINGS OF RIKEN BNL RESEARCH CENTER WORKSHOP, VOLUME 19},

author = {BLUM,T.},

abstractNote = {The RIKEN BNL Research Center hosted its 19th workshop April 27th through May 1, 1999. The topic was Numerical Algorithms at Non-Zero Chemical Potential. QCD at a non-zero chemical potential (non-zero density) poses a long-standing unsolved challenge for lattice gauge theory. Indeed, it is the primary unresolved issue in the fundamental formulation of lattice gauge theory. The chemical potential renders conventional lattice actions complex, practically excluding the usual Monte Carlo techniques which rely on a positive definite measure for the partition function. This ''sign'' problem appears in a wide range of physical systems, ranging from strongly coupled electronic systems to QCD. The lack of a viable numerical technique at non-zero density is particularly acute since new exotic ''color superconducting'' phases of quark matter have recently been predicted in model calculations. A first principles confirmation of the phase diagram is desirable since experimental verification is not expected soon. At the workshop several proposals for new algorithms were made: cluster algorithms, direct simulation of Grassman variables, and a bosonization of the fermion determinant. All generated considerable discussion and seem worthy of continued investigation. Several interesting results using conventional algorithms were also presented: condensates in four fermion models, SU(2) gauge theory in fundamental and adjoint representations, and lessons learned from strong; coupling, non-zero temperature and heavy quarks applied to non-zero density simulations.},

doi = {10.2172/14643},

journal = {},

number = ,

volume = ,

place = {United States},

year = {1999},

month = {9}

}