论文标题
通往能源差距的三条道路
Three roads to the energy gap
论文作者
论文摘要
我们通过分析确定有吸引力的多组分Gaudin-Yang模型中弱耦合处的能量差距，这是一个可集成的模型，该模型描述了与$κ$成分的一个维度相互作用的费米子。我们使用三种不同的方法。第一个是基于对Bethe Ansatz方程的直接分析。第二种方法使用了基态能量的复兴理论和扰动序列的大阶行为。第三种方法基于重新归一化组分析。这三种方法导致了相同的答案，以这种方式提供了对复兴和雷诺马隆的思想的非平凡检验，应用于非权威主义的多体系统。
We determine analytically the energy gap at weak coupling in the attractive multi-component Gaudin--Yang model, an integrable model which describes interacting fermions in one dimension with $κ$ components. We use three different methods. The first one is based on a direct analysis of the Bethe ansatz equations. The second method uses the theory of resurgence and the large order behavior of the perturbative series for the ground state energy. The third method is based on a renormalization group analysis. The three methods lead to the same answer, providing in this way a non-trivial test of the ideas of resurgence and renormalons as applied to non-relativistic many-body systems.
