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 (CNπ). In order to reduce the number of contractions required in calculating CNπ 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 ρI ≈ 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, mπ ≤ μI ≤ 4.5 mπ. 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 μI ≥ mπ.