Peierls Transition in Gross-Neveu Model from Bethe Ansatz,Physical Review Letters

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Peierls Transition in Gross-Neveu Model from Bethe Ansatz
Physical Review Letters ( IF 8.1 ) Pub Date : 2024-09-03 , DOI: 10.1103/physrevlett.133.101601
Valdemar Melin ₁ , Yuta Sekiguchi _{1,

2} , Paul Wiegmann ₃ , Konstantin Zarembo _{1,

2,

4}

Affiliation

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.

Published by the American Physical Society

2024

中文翻译：

来自 Bethe Ansatz 的 Gross-Neveu 模型中的 Peierls 过渡

二维 Gross-Neveu 模型预计将在高重子电荷密度下发生晶体相变。这个结论是从平均场近似中得出的，它与 Peierls 不稳定性模型非常相似。我们证明，当对称群的秩和影响重子密度的粒子表示的维度都很大（较大的 N 极限）时，这种转变确实会发生。我们通过模型的精确解得出这个结果，开发 Bethe ansatz 的大 N 极限。我们对 Bethe ansatz 方程的大 N 解的解析构造与平均场分析的 Korteweg-de Vries （KdV）的周期性（有限间隙）解完全一致。美国物理学会 2024 年出版

更新日期：2024-09-03

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