LQCD 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 $N{\pi }^{+}$'s ($C_{N\pi }$). In order to reduce the number of contractions required in calculating $C_{N\pi }$ 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 $390\mathrm{MeV}$, and with lattice spatial extents $L\sim 2.0,2.5,3.0\mathrm{fm}$. The largest isospin density of ${\rho }_I\approx 9{\mathrm{fm}}^{-3}$ is achieved in the smallest volume, and the QCD phase diagram is investigated at a fixed low temperature at varying isospin chemical potentials, $m_{\pi }\le {\mu }_I\le 4.5m_{\pi }$. 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 ${\mu }_I\ge m_{\pi }$.

Comments: 5 pages, 4 figures