The extended Hubbard model with an attractive density-density interaction, positive pair hopping, or both, is shown to host topological phases, with a doubly degenerate entanglement spectrum and interacting edge spins. This constitutes a novel instance of topological order which emerges from interactions. When the interaction terms combine in a charge-SU(2) symmetric fashion, a novel partially polarized pseudospin phase appears, in which the topological features of the spin degrees of freedom coexist with long-range $\eta$-wave superconductivity. Thus, our system provides an example of an interplay between spontaneous symmetry breaking and symmetry-protected topological order that leads to novel and unexpected properties.

中文翻译：

---

扩展哈伯德模型中由吸引力相互作用和跳对引起的拓扑相

具有有吸引力的密度-密度相互作用、正对跳跃或两者兼有的扩展哈伯德模型显示出具有双简并纠缠谱和相互作用的边缘自旋的拓扑相。这构成了从相互作用中出现的拓扑顺序的新实例。当相互作用项以电荷-SU(2) 对称方式结合时，会出现一种新的部分极化赝自旋相，其中自旋自由度的拓扑特征与长程 $\eta$ 波超导性共存。因此，我们的系统提供了一个自发对称破坏和对称保护拓扑顺序之间相互作用的例子，这导致了新的和意想不到的特性。