Effect of $U_A(1)$ Breaking on Chiral Phase Structure and Pion   Superfluidity at Finite Isospin Chemical Potential
  We investigate the isospin chemical potential effect in the frame of SU(2) Nambu-Jona-Lasinio model. When the isospin chemical potential is less than the vacuum pion mass, the phase structure with two chiral phase transition lines does not happen due to $U_A(1)$ breaking of QCD. When the isospin chemical potential is larger than the vacuum pion mass, the ground state of the system is a Bose-Einstein condensate of charged pions. 
Lianyi He, Meng Jin and Pengfei Zhuang