Chiral density waves in the NJL$_2$ model with quark number and isospin chemical potentials

Understand

We investigate the phase portrait of the (1+1)-dimensional massless two-flavored NJL$_2$ model containing a quark number chemical potential $\mu$ and an isospin chemical potential $\mu_I$ in the limit of a large number of colors $N_c\to\infty$.

• Particular attention is paid to the question to what extent the inclusion of an isospin asymmetry affects chiral condensates to have a spatial inhomogeneity in the form of the so-called chiral density waves (CDW) (chiral spirals).
• It is shown that at zero temperature and comparatively small values of $\mu$, i.e.
• at $\mu<\mu_c\approx 0.68M_0$ ($M_0$ is the dynamical quark mass in the vacuum) only the homogeneous charged pion condensation phase is realized for arbitrary nonzero values of $\mu_I$.