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 + 1)-dimensional Nambu-Jona-Lasinio model in the large-N-c limit at finite temperature T and quark chemical potential mu using dimensional regularization. The phase diagram in the mu-T plane is mapped out. At zero temperature, an inhomogeneous phase with a chiral-density wave exists for mu > mu(c), where mu(c) 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 mu(I). The phase diagram in the mu(I) - mu plane is mapped out and shows a rich phase structure.