Chiral density wave versus pion condensation in the (1+1)-dimensional NJL model

In this paper, we study the possibility of an inhomogeneous quark condensate in the (1 þ 1)-dimensional Nambu-Jona-Lasinio model in the large-Nc limit at finite temperature T and quark chemical potential μ using dimensional regularization. The phase diagram in the μ–T plane is mapped out. At zero temperature, an inhomogeneous phase with a chiral-density wave exists for μ > μc, where μc is a critical chemical potential. Performing a Ginzburg-Landau analysis, we show that in the chiral limit, the tricritical point and the Lifschitz point coincide. We also consider the competition between a chiral-density wave and a constant pion condensate at finite isospin chemical potential μI. The phase diagram in the μI − μ plane is mapped out and shows a rich phase structure