We study Hilbert space fragmentation in the extended Fermi-Hubbard model with nearest and next-nearest neighbor interactions. Using a generalized spin/mover picture and saddle point methods, we derive lower bounds for the scaling of the number of frozen states and for the size of the largest block preserved under the dynamics. We find fragmentation for strong nearest and next-nearest neighbor repulsions as well as for the combined case. Our results suggest that the involvement of next-nearest neighbor repulsions leads to an increased tendency for localization. We then model the dynamics for larger systems using Markov simulations to test these findings and unveil in which interaction regimes the dynamics becomes spatially localized. In particular, we show that for strong nearest and next-nearest neighbor interactions random initial states will localize provided that the density of initial movers is sufficiently low.

中文翻译：

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扩展费米-哈伯德模型中的希尔伯特空间碎片和相互作用引起的定位

我们研究了扩展的 Fermi-Hubbard 模型中的 Hilbert 空间碎片，该模型具有最近和次最近邻交互。使用广义的自旋/移动图像和鞍点方法，我们推导出冻结状态数量的缩放和在动力学下保留的最大块的大小的下界。我们发现了强烈的最近和次近邻居排斥以及组合情况的碎片。我们的结果表明，下一个最近邻居排斥的参与导致本地化趋势增加。然后，我们使用马尔可夫模拟对更大系统的动力学进行建模，以测试这些发现并揭示动力学在哪些相互作用机制中成为空间局部化的。尤其是，