Functional renormalization group study of ρ meson condensate at a finite isospin chemical potential in the quark meson model*

We investigated the effect of an isospin chemical potential ( ) within the quark-meson model, which approximates quantum chromodynamics (QCD) by modeling low-energy phenomena such as chiral symmetry breaking and phase structure under varying conditions of temperature and chemical potential. Using the functional renormalization group (FRG) flow equations, we calculated the phase diagram in the chiral limit within the two-flavor quark-meson model in a finite with ρ vector meson interactions. Fluctuation effects significantly decrease the critical chemical potential from the mean-field (MF) value to a lower value at which the ρ vector meson condensates alongside the chiral condensate once the isospin chemical potential exceeds the critical value . This ρ condensation was investigated numerically for different meson coupling strengths. The ρ meson dominated region is delineated from other phases by a second-order phase transition at lower and a first-order transition at slightly higher .