Lattice QCD at finite isospin density at zero and finite temperature

Abstract

We simulate lattice QCD with dynamical $u$ and $d$ quarks at finite chemical potential, $μ_I$, for the third component of isospin ($I_3$), at both zero and at finite temperature. At zero temperature there is some $μ_I$, $μ_c$ say, above which $I_3$ and parity are spontaneously broken by a charged pion condensate. This is in qualitative agreement with the prediction of effective (chiral) Lagrangians which also predict $μ_c=m_π$. This transition appears to be second order, with scaling properties consistent with the mean-field predictions of such effective Lagrangian models. We have also studied the restoration of $I_3$ symmetry at high temperature for $μ_I > μ_c$. For $μ_I$ sufficiently large, this finite temperature phase transition appears to be first order. As $μ_I$ is decreased it becomes second order connecting continuously with the zero temperature transition.