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Recently the revised phase diagram of the (large N) Gross-Neveu model in 1 + 1 dimensions with discrete chiral symmetry has been determined numerically. It features three phases, a massless and a massive Fermi gas and a kink-antikink crystal. Here we investigate the phase diagram by analytical means, mapping the Dirac-Hartree-Fock equation onto the non-relativistic Schrö dinger equation with the (single gap) Lamé potential. It is pointed out that mathematically identical phase diagrams appeared in the condensed matter literature some time ago in the context of the Peierls-Frö hlich model and ferromagnetic superconductors.

Abstract. During the last few years, the phase diagram of the large N Gross-Neveu model in 1+1 dimensions at finite temperature and chemical potential has undergone a major revision. Here we present a streamlined account of this development, collecting the most important results. Quasi-one-dimensional condensed matter systems like conducting polymers provide real physical systems which can be approximately described by the Gross-Neveu model and have played some role in establishing its phase structure. The kink-antikink phase found at low temperatures is closely related to inhomogeneous superconductors in the Larkin-Ovchinnikov-Fulde-Ferrell phase. With the complete phase diagram at hand, the Gross-Neveu model can now serve as a firm testing ground for new algorithms and theoretical ideas.

We study two-dimensional, large N field theoretic models (Gross-Neveu model, 't Hooft model) at finite baryon density near the chiral limit. The same mechanism which leads to massless baryons in these models induces a breakdown of translational invariance at any finite density. In the chiral limit baryonic matter is characterized by a spatially varying chiral angle with a wave number depending only on the density. For small bare quark masses a sine-Gordon kink chain is obtained which may be regarded as simplest realization of the Skyrme crystal for nuclear matter. Characteristic differences between confining and non-confining models are pointed out. 1) IntroductionThe description of baryonic matter on the basis of QCD remains a theoretical challenge, especially since lattice gauge calculations have so far been of little help for this problem. Nuclear physics, relativistic heavy-ion physics and astrophysics are some of the fields which would greatly benefit from any progress on this issue. Recently, a new surge of interest has been triggered by the suggestion that at high density, the novel phenomenon of color superconductivity might set in [1, 2]. This development has highlighted how little is known reliably about dense, strongly interacting matter.Here, we address a much simpler finite density problem where a full analytic solution can be found: We consider two-dimensional model field theories with interacting fermions at or near the chiral limit. Specifically, we have in mind the two-dimensional version of the Nambu-Jona-Lasinio model [3], i.e., the chiral Gross-Neveu model [4], and QCD 2 with fundamental quarks, the 't Hooft model [5]. In both cases, one considers a large number N of fermion species and investigates the limit N → ∞, keeping Ng 2 fixed [6]. These two models are quite similar as far as their chiral properties are concerned but differ with respect to confinement of quarks which is only exhibited by the 't Hooft model. So far, the phase diagram of the Gross-Neveu model has been studied extensively as function of temperature and chemical potential [7, 8, 9, 10, 11], and the results seem to be uncontroversial. The 't Hooft model on the other hand has been investigated only sporadically at finite temperature [20,21], most recently in Ref. [22], but hardly anything is known yet about its properties at finite density [21].Our point of departure is the following observation: Both of these models possess light baryons whose mass vanishes in the chiral limit [23,24,25] (by light, we mean that M B /N is small on the relevant physical scale). This is of course no accident, but a generic feature of models with broken chiral symmetry in 1+1 dimension -the baryons are topologically non-trivial excitations of the Goldstone boson ("pion") field. By contrast, the Gross-Neveu model with discrete chiral symmetry can only accommodate baryons whose mass scales with the physical fermion mass and hence stays finite in the chiral limit. Nevertheless, it has been argued that both variants of the Gross-Neveu mode...

We confirm earlier hints that the conventional phase diagram of the discrete chiral Gross-Neveu model in the large N limit is deficient at non-zero chemical potential. We present the corrected phase diagram constructed in mean field theory. It has three different phases, including a kink-antikink crystal phase. All transitions are second order. The driving mechanism for the new structure of baryonic matter in the Gross-Neveu model is an Overhauser type instability with gap formation at the Fermi surface.