Crystalline ground state in chiral Gross-Neveu and Cooper pair models at finite densities

Abstract

We study the possibility of a spatially nonuniform ground state in (1+1)-dimensional models with quartic Fermi interactions at finite fermion densities by introducing the chemical potential μ. We examine the chiral Gross-Neveu model and the Cooper pair model as toy models of chiral symmetry breaking and the difermion pair condensates which are presumed to exist in QCD. We confirm in the chiral Gross-Neveu model that the ground state has a crystalline structure in which the chiral condensate oscillates in space with a wave number 2μ, whereas in the Cooper pair model we find that the vacuum structure is spatially uniform. Some discussion is given to explain this difference.