# Progress on Complex Langevin simulations of a finite density matrix model for QCD

## Abstract

We study the Stephanov model, which is an RMT model for QCD at finite density, using the Complex Langevin algorithm. Naive implementation of the algorithm shows convergence towards the phase quenched or quenched theory rather than to intended theory with dynamical quarks. A detailed analysis of this issue and a potential resolution of the failure of this algorithm are discussed. We study the effect of gauge cooling on the Dirac eigenvalue distribution and time evolution of the norm for various cooling norms, which were specifically designed to remove the pathologies of the complex Langevin evolution. The cooling is further supplemented with a shifted representation for the random matrices. Unfortunately, none of these modifications generate a substantial improvement on the complex Langevin evolution and the final results still do not agree with the analytical predictions.

- Authors:

- Univ. of Regensburg (Germany). Inst. for Theorectical Physics
- Swansea Univ., Swansea U.K.
- Stony Brook Univ., NY (United States). Dept. of Physics and Astronomy
- Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); College of William and Mary, Williamsburg, VA (United States); Heidelberg Univ. (Germany). Inst. for Theoretische Physik

- Publication Date:

- Research Org.:
- Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)

- OSTI Identifier:
- 1434244

- Report Number(s):
- JLAB-THY-18-2693; DOE/OR/23177-4425; arXiv:1801.06456

- DOE Contract Number:
- AC05-06OR23177; NSF PHY-1516509

- Resource Type:
- Conference

- Resource Relation:
- Journal Name: EPJ Web of Conferences; Journal Volume: 175; Conference: Lattice 2017, 35th International Symposium on Lattice Field Theory, 18-24 Jun 2017. Granada, Spain

- Country of Publication:
- United States

- Language:
- English

### Citation Formats

```
Bloch, Jacques, Glesaan, Jonas, Verbaarschot, Jacobus, and Zafeiropoulos, Savvas.
```*Progress on Complex Langevin simulations of a finite density matrix model for QCD*. United States: N. p., 2018.
Web. doi:10.1051/epjconf/201817507034.

```
Bloch, Jacques, Glesaan, Jonas, Verbaarschot, Jacobus, & Zafeiropoulos, Savvas.
```*Progress on Complex Langevin simulations of a finite density matrix model for QCD*. United States. doi:10.1051/epjconf/201817507034.

```
Bloch, Jacques, Glesaan, Jonas, Verbaarschot, Jacobus, and Zafeiropoulos, Savvas. Sun .
"Progress on Complex Langevin simulations of a finite density matrix model for QCD". United States.
doi:10.1051/epjconf/201817507034. https://www.osti.gov/servlets/purl/1434244.
```

```
@article{osti_1434244,
```

title = {Progress on Complex Langevin simulations of a finite density matrix model for QCD},

author = {Bloch, Jacques and Glesaan, Jonas and Verbaarschot, Jacobus and Zafeiropoulos, Savvas},

abstractNote = {We study the Stephanov model, which is an RMT model for QCD at finite density, using the Complex Langevin algorithm. Naive implementation of the algorithm shows convergence towards the phase quenched or quenched theory rather than to intended theory with dynamical quarks. A detailed analysis of this issue and a potential resolution of the failure of this algorithm are discussed. We study the effect of gauge cooling on the Dirac eigenvalue distribution and time evolution of the norm for various cooling norms, which were specifically designed to remove the pathologies of the complex Langevin evolution. The cooling is further supplemented with a shifted representation for the random matrices. Unfortunately, none of these modifications generate a substantial improvement on the complex Langevin evolution and the final results still do not agree with the analytical predictions.},

doi = {10.1051/epjconf/201817507034},

journal = {EPJ Web of Conferences},

number = ,

volume = 175,

place = {United States},

year = {Sun Apr 01 00:00:00 EDT 2018},

month = {Sun Apr 01 00:00:00 EDT 2018}

}