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
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913461172174848 |
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| author | Koenigstein, Adrian Winstel, Marc |
| author_facet | Koenigstein, Adrian Winstel, Marc |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_03459 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | 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 Koenigstein, Adrian Winstel, Marc High Energy Physics - Theory Strongly Correlated Electrons High Energy Physics - Phenomenology 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. |
| title | 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 |
| topic | High Energy Physics - Theory Strongly Correlated Electrons High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2405.03459 |