Inhomogeneous condensates in the thermodynamics of the chiralNJL2model

Abstract

We analyze the thermodynamical properties, at finite density and nonzero temperature, of the ($1+1$) dimensional chiral Gross-Neveu model (the ${\mathrm{NJL}}_{2}$ model), using the exact inhomogeneous (crystalline) condensate solutions to the gap equation. The continuous chiral symmetry of the model plays a crucial role, and the thermodynamics leads to a broken phase with a periodic spiral condensate, the ``chiral spiral,'' as a thermodynamically preferred limit of the more general ``twisted kink crystal'' solution of the gap equation. This situation should be contrasted with the Gross-Neveu model, which has a discrete chiral symmetry, and for which the phase diagram has a crystalline phase with a periodic kink crystal. We use a combination of analytic, numerical, and Ginzburg-Landau techniques to study various parts of the phase diagram.