# Lattice QCD at non-zero isospin chemical potential

## Abstract

Quantum chromodynamics (QCD) at non-zero isospin chemical potential is studied in a canonical approach by analyzing systems of fixed isospin number density. To construct these systems, we develop a range of new algorithms for performing the factorially large numbers of Wick contractions required in multi-hadron systems. We then use these methods to study systems with the quantum numbers of up to 72 $$\pi^+$$'s on three ensembles of gauge configurations with spatial extents L ~ 2.0, 2.5 and 3.0 fm, and light quark masses corresponding to a pion mass of 390 MeV. The ground state energies of these systems are extracted and the volume dependence of these energies is utilized to determine the two- and three- body interactions amongst $$\pi^+$$'s. The systems studied correspond to isospin densities of up to $$\rho_I ~ 9 fm^{-3}$$ and probe isospin chemical potentials, $$\mu_I$$, in the range $$m_\pi\ \lsim \mu_I\ \lsim 4.5\ m_\pi$$, allowing us to investigate aspects of the QCD phase diagram at low temperature and for varying isospin chemical potential. By studying the energy density of the system, we provide numerical evidence for the conjectured transition of the system to a Bose-Einstein condensed phase at $$\mu_I\ \gsim m_\pi$$.

- 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:
- 1054927

- Report Number(s):
- JLAB-THY-12-1548; DOE/OR/23177-2133; arXiv:1205.4224

- DOE Contract Number:
- AC05-06OR23177

- Resource Type:
- Journal Article

- Journal Name:
- Phys. Rev. D

- Additional Journal Information:
- Journal Volume: 86; Journal Issue: 05

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
William Detmold, Konstantinos Orginos, Zhifeng Shi.
```*Lattice QCD at non-zero isospin chemical potential*. United States: N. p., 2012.
Web. doi:10.1103/PhysRevD.86.054507.

```
William Detmold, Konstantinos Orginos, Zhifeng Shi.
```*Lattice QCD at non-zero isospin chemical potential*. United States. https://doi.org/10.1103/PhysRevD.86.054507

```
William Detmold, Konstantinos Orginos, Zhifeng Shi. Sat .
"Lattice QCD at non-zero isospin chemical potential". United States. https://doi.org/10.1103/PhysRevD.86.054507.
```

```
@article{osti_1054927,
```

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

author = {William Detmold, Konstantinos Orginos, Zhifeng Shi},

abstractNote = {Quantum chromodynamics (QCD) at non-zero isospin chemical potential is studied in a canonical approach by analyzing systems of fixed isospin number density. To construct these systems, we develop a range of new algorithms for performing the factorially large numbers of Wick contractions required in multi-hadron systems. We then use these methods to study systems with the quantum numbers of up to 72 $\pi^+$'s on three ensembles of gauge configurations with spatial extents L ~ 2.0, 2.5 and 3.0 fm, and light quark masses corresponding to a pion mass of 390 MeV. The ground state energies of these systems are extracted and the volume dependence of these energies is utilized to determine the two- and three- body interactions amongst $\pi^+$'s. The systems studied correspond to isospin densities of up to $\rho_I ~ 9 fm^{-3}$ and probe isospin chemical potentials, $\mu_I$, in the range $m_\pi\ \lsim \mu_I\ \lsim 4.5\ m_\pi$, allowing us to investigate aspects of the QCD phase diagram at low temperature and for varying isospin chemical potential. By studying the energy density of the system, we provide numerical evidence for the conjectured transition of the system to a Bose-Einstein condensed phase at $\mu_I\ \gsim m_\pi$.},

doi = {10.1103/PhysRevD.86.054507},

url = {https://www.osti.gov/biblio/1054927},
journal = {Phys. Rev. D},

number = 05,

volume = 86,

place = {United States},

year = {2012},

month = {9}

}