Peierls Transition in Gross-Neveu Model from Bethe Ansatz
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929473602977792 |
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| author | Melin, Valdemar Sekiguchi, Yuta Wiegmann, Paul Zarembo, Konstantin |
| author_facet | Melin, Valdemar Sekiguchi, Yuta Wiegmann, Paul Zarembo, Konstantin |
| contents | The two-dimensional Gross-Neveu model is anticipated to undergo a crystalline phase transition at high baryon charge densities. This conclusion is drawn from the mean-field approximation, which closely resembles models of Peierls instability. We demonstrate that this transition indeed occurs when both the rank of the symmetry group and the dimension of the particle representation contributing to the baryon density are large (the large-N limit). We derive this result through the exact solution of the model, developing the large-N limit of the Bethe Ansatz. Our analytical construction of the large-N solution of the Bethe Ansatz equations aligns perfectly with the periodic (finite-gap) solution of the Korteweg-de Vries (KdV) of the mean-field analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_07307 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Peierls Transition in Gross-Neveu Model from Bethe Ansatz Melin, Valdemar Sekiguchi, Yuta Wiegmann, Paul Zarembo, Konstantin High Energy Physics - Theory The two-dimensional Gross-Neveu model is anticipated to undergo a crystalline phase transition at high baryon charge densities. This conclusion is drawn from the mean-field approximation, which closely resembles models of Peierls instability. We demonstrate that this transition indeed occurs when both the rank of the symmetry group and the dimension of the particle representation contributing to the baryon density are large (the large-N limit). We derive this result through the exact solution of the model, developing the large-N limit of the Bethe Ansatz. Our analytical construction of the large-N solution of the Bethe Ansatz equations aligns perfectly with the periodic (finite-gap) solution of the Korteweg-de Vries (KdV) of the mean-field analysis. |
| title | Peierls Transition in Gross-Neveu Model from Bethe Ansatz |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2404.07307 |