On the Inhomogeneous Phase of the Chiral Gross-Neveu Model

Abstract

There is substantial evidence that the ground state of the 2d chiral Gross-Neveu model, in the presence of a $U(1)$ fermion number chemical potential $\mu$ and in the large $N$ limit, is given by a {\it chiral spiral} phase, namely an inhomogeneous phase with a chiral condensate having a spatially periodic phase. We show that the chiral spiral configuration persists at finite $N$ and $T=0$ for any $\mu >0$. Our analysis is based on non-abelian bosonization, that relates the model to a $U(N{)}_1$ WZW model deformed by current-current interactions. In this description the appearance of the inhomogeneous phase is surprisingly simple. We also rederive the phase diagram of the large $N$ chiral Gross-Neveu model via a direct diagrammatic computation, finding agreement with previous results in the literature.

6 pages, one figure; v2: several improvements, matches version accepted by PRL

References in corpus (6)

• Inhomogeneous chiral condensates
• Topological Transition on the Conformal Manifold
• Inhomogeneous phases in the Gross-Neveu model in 1+1 dimensions at finite number of flavors
• Phase diagram of the large $N$ Gross-Neveu model in a finite periodic box
• Inhomogeneities in the $2$-Flavor Chiral Gross-Neveu Model
• When cold, dense quarks in 1+1 and 3+1 dimensions are not a Fermi liquid