Peierls Transition in Gross-Neveu Model from Bethe Ansatz (2404.07307v2)
Abstract: 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.
- D. J. Gross and A. Neveu, Phys. Rev. D 10, 3235 (1974).
- A. B. Zamolodchikov and A. B. Zamolodchikov, Annals Phys. 120, 253 (1979).
- M. Karowski and H. J. Thun, Nucl. Phys. B 190, 61 (1981).
- M. Thies and K. Urlichs, Phys. Rev. D 67, 125015 (2003), arXiv:hep-th/0302092 .
- M. Thies, J. Phys. A 39, 12707 (2006), arXiv:hep-th/0601049 .
- R. E. Peierls, Quantum theory of solids (Oxford University Press, 1955).
- H. Fröhlich, Proc. R. Soc. A223, 296 (1954).
- B. Horovitz, Phys. Rev. Lett. 46, 742 (1981).
- M. Nakahara and K. Maki, Phys. Rev. B 24, 1045 (1981).
- S. Brazovskii and N. Kirova, Sov. Sci. Rev. A 5, 99 (1984).
- E. Witten, Nucl. Phys. B 145, 110 (1978a).
- V. L. Berezinskii, Sov. Phys. JETP 32, 493 (1971).
- J. M. Kosterlitz and D. J. Thouless, J. Phys. C 6, 1181 (1973).
- E. Witten, Nucl. Phys. B 142, 285 (1978b).
- R. Jackiw and C. Rebbi, Phys. Rev. D 13, 3398 (1976).
- A. Chodos and H. Minakata, Nucl. Phys. B 490, 687 (1997), arXiv:hep-th/9610150 .
- M. Mariño and T. Reis, JHEP 04, 160 (2020), arXiv:1909.12134 [hep-th] .
- F. Gakhov, Boundary value problems (Dover Publications, 1990).