Revisiting the spatially inhomogeneous condensates in the $(1 + 1)$-dimensional chiral Gross-Neveu model via the bosonic two-point function in the infinite-$N$ limit

Abstract

This work shows that the known phase boundary between the phase with chiral symmetry and the phase of spatially inhomogeneous chiral symmetry breaking in the phase diagram of the $(1 + 1)$-dimensional chiral Gross-Neveu model can be detected from the bosonic two-point function alone and thereby confirms and extends previous results arXiv:hep-th/0008175, arXiv:0807.2571, arXiv:0909.3714, arXiv:1810.03921, arXiv:2203.08503. The analysis is referred to as the stability analysis of the symmetric phase and does not require knowledge about spatial modulations of condensates. We perform this analysis in the infinite-$N$ limit at nonzero temperature and nonzero quark and chiral chemical potentials also inside the inhomogeneous phase. Thereby we observe an interesting relation between the bosonic $1$-particle irreducible two-point vertex function of the chiral Gross-Neveu model and the spinodal line of the Gross-Neveu model.