On the origin of the peak of the sound velocity for isospin imbalanced strongly interacting matter

We study the properties of a system composed of strongly interacting matter with an isospin imbalance, using as an effective description of QCD the two-flavor Linear Sigma Model with quarks. From the one-loop effective potential, including the two light quarks, pions and sigma contributions, and enforcing the restrictions imposed by chiral symmetry, we show that the development of an isospin condensate comes together with the emergence of a Goldstone mode that provides a constraint for the chiral and isospin condensates as a result of a non-trivial mixing between the charged pions and the sigma. We compute the thermodynamical quantities of interest and in particular the sound velocity squared, showing that it presents a maximum for an isospin chemical potential similar to the one reported by lattice QCD results and also with a similar height. Therefore, we attribute the origin of the peak of the sound velocity to the proper treatment of the Goldstone mode and to the non-trivial mixing of the charged pions and sigma in the isospin condensed phase.