论文标题
多游戏哈伯德模型中的三体问题
Three-body problem in a multiband Hubbard model
论文作者
论文摘要
我们在通用的多型晶格中考虑了三体问题，并分析了由两个旋转的三聚体的分散 - $ \ uparrow $ fermions和一个旋转 - $ \ $ \ downarrow $ fermion，由于介于两者之间的现场吸引力。基于变异方法，我们首先以一组耦合积分方程的形式获得精确的解，然后将其减少到特征值问题。作为例证，我们将理论应用于锯齿晶格，并在数值上表明允许在两种频段设置中进行能量稳定的三聚体，该设置与单波段线性链模型形成鲜明对比。特别是我们还揭示了三聚体在平坦带中形成时具有近乎流动的分散体，这与其二聚体的高度分散频谱不同。
We consider the three-body problem in a generic multiband lattice, and analyze the dispersion of the trimer states that are made of two spin-$\uparrow$ fermions and a spin-$\downarrow$ fermion due to an onsite attraction in between. Based on a variational approach, we first obtain the exact solution in the form of a set of coupled integral equations, and then reduce it to an eigenvalue problem. As an illustration we apply our theory to the sawtooth lattice, and numerically show that energetically-stable trimers are allowed in a two-band setting, which is in sharp contrast with the single-band linear-chain model. In particular we also reveal that the trimers have a nearly-flat dispersion when formed in a flat band, which is unlike the highly-dispersive spectrum of its dimers.
