Inhomogeneous charged pion condensation in chiral asymmetric dense quark matter in the framework of NJL$_2$ model

Understand

In this paper we investigate the phase structure of a (1+1)-dimensional quark model with four-quark interaction and in the presence of baryon ($\mu_B$), isospin ($\mu_I$) and chiral isospin ($\mu_{I5}$) chemical potentials.

• Spatially inhomogeneous chiral density wave (for chiral condensate) and single wave (for charged pion condensate) approaches are used.
• It is established that in the large-$N_c$ limit ($N_c$ is the number of colored quarks) there exists a duality correspondence between the chiral symmetry breaking phase and the charged pion condensation (PC) one.
• Moreover, it is shown that inhomogeneous charged PC phase with nonzero baryon density is induced in the model by arbitrary small values of the chemical potential $\mu_{I5}$ (for a rather large region of $\mu_B$ and $\mu_I$).