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Updated: Aug 30, 2025

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Inhomogeneous Phase of the Chiral Gross-Neveu Model
Riccardo Ciccone1, Lorenzo Di Pietro2, Marco Serone1
1SISSA, via Bonomea 265, 34136 Trieste, Italy and INFN, Sezione di Trieste, via Valerio 2, 34127 Trieste, Italy.
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 μ and in the large N limit, is given by a "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 μ>0. Our analysis is based on nonabelian bosonization, that relates the model to a U(N)_{1} Wess-Zumino-Witten 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.
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