In this paper we present the example the details of the transition of the Hubbard model to the Heisenberg model in the limit of on-site repulsion constant u → ∞. We explore the models with respect to the nearest and the next-nearest-neighbour hopping. We construct the next-nearest-neighbour hopping free subspaces for the considered example and find the procedure applicable to any number and any configuration of electrons in the chain. We found that some eigenvalues permute themselves for a specific value of the ratio of on-site repulsion constant to hopping constant and the effect is more visible the greater the next-nearest-neighbour hopping is. A similar situation occurs for eigenvectors. We also confirm SU(2)× SU(2) symmetry breaking when the next-nearest-neighbour hopping are considered.

在本文中，我们通过示例详细介绍了在现场排斥常数u → ∞ 的限制下从哈伯德模型过渡到海森堡模型的细节。我们探索了关于最近和下一个最近邻跳跃的模型。我们为所考虑的示例构建了下一个最近邻跳跃自由子空间，并找到适用于链中任何数量和任何配置的电子的过程。我们发现一些特征值会根据现场排斥常数与跳跃常数之比的特定值自行置换，并且下一个最近邻跳跃越大，效果越明显。特征向量也会出现类似的情况。当考虑下一个最近邻跳跃时，我们还确认 SU(2)× SU(2) 对称性破缺。