# Lattice QCD at non-zero isospin chemical potential

## Abstract

Systems of non-zero isospin chemical potential are studied from a canonical approach by computing correlation functions with the quantum numbers of N π(+)'s (C(N)(π)). In order to reduce the number of contractions required in calculating C(N)(π) for a large N in the Wick's theorem, we constructed a few new algorithms. With these new algorithms, systems with isospin charge up to 72 are investigated on three anisotropic gauge ensembles with a pion mass of 390 MeV, and with lattice spatial extents L ~ 2.0, 2.5, 3.0 fm. The largest isospin density of ρ(I) thickapprox 9 fm(-)(3) is achieved in the smallest volume, and the QCD phase diagram is investigated at a fixed low temperature at varying isospin chemical potentials, m(π) ≤ μ(I) ≤ 4.5 m(π). By investigating the behaviour of the extracted energy density of the system at different isospin chemical potentials, we numerically identified the conjectured transition to a Bose-Einstein condensation state at μ(I) ≥ m(π).

- Authors:

- Publication Date:

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

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1079969

- Report Number(s):
- JLAB-THY-12-1678; DOE/OR/23177-2566

Journal ID: ISSN 1742-6588

- DOE Contract Number:
- AC05-06OR23177

- Resource Type:
- Conference

- Journal Name:
- Journal of Physics. Conference Series

- Additional Journal Information:
- Journal Volume: 432; Conference: Extreme QCD 2012 (XQCD12), 21-23 Aug 2012. Washington, USA; Journal ID: ISSN 1742-6588

- Publisher:
- IOP Publishing

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Shi, Zhifeng.
```*Lattice QCD at non-zero isospin chemical potential*. United States: N. p., 2013.
Web. doi:10.1088/1742-6596/432/1/012026.

```
Shi, Zhifeng.
```*Lattice QCD at non-zero isospin chemical potential*. United States. https://doi.org/10.1088/1742-6596/432/1/012026

```
Shi, Zhifeng. Tue .
"Lattice QCD at non-zero isospin chemical potential". United States. https://doi.org/10.1088/1742-6596/432/1/012026.
```

```
@article{osti_1079969,
```

title = {Lattice QCD at non-zero isospin chemical potential},

author = {Shi, Zhifeng},

abstractNote = {Systems of non-zero isospin chemical potential are studied from a canonical approach by computing correlation functions with the quantum numbers of N π(+)'s (C(N)(π)). In order to reduce the number of contractions required in calculating C(N)(π) for a large N in the Wick's theorem, we constructed a few new algorithms. With these new algorithms, systems with isospin charge up to 72 are investigated on three anisotropic gauge ensembles with a pion mass of 390 MeV, and with lattice spatial extents L ~ 2.0, 2.5, 3.0 fm. The largest isospin density of ρ(I) thickapprox 9 fm(-)(3) is achieved in the smallest volume, and the QCD phase diagram is investigated at a fixed low temperature at varying isospin chemical potentials, m(π) ≤ μ(I) ≤ 4.5 m(π). By investigating the behaviour of the extracted energy density of the system at different isospin chemical potentials, we numerically identified the conjectured transition to a Bose-Einstein condensation state at μ(I) ≥ m(π).},

doi = {10.1088/1742-6596/432/1/012026},

url = {https://www.osti.gov/biblio/1079969},
journal = {Journal of Physics. Conference Series},

issn = {1742-6588},

number = ,

volume = 432,

place = {United States},

year = {2013},

month = {4}

}