论文标题
希尔伯特的空间碎片和相互作用引起的局部定位
Hilbert space fragmentation and interaction-induced localization in the extended Fermi-Hubbard model
论文作者
论文摘要
我们在扩展的费米 - 哈伯德模型中研究了希尔伯特空间碎片，其最接近和下一个最邻居的相互作用。使用广义的自旋/移动图像和鞍点方法，我们为冷冻状态数量的缩放和动力学下保留的最大块的大小得出了下限。我们发现碎裂的最近和下一期最新的排斥力以及联合案例的碎片化。我们的结果表明，次要邻居排斥的参与会导致局部化的趋势增加。然后，我们使用Markov模拟对较大系统的动力学进行建模，以测试这些发现并揭开在该发现的相互作用方案在空间上局部定位的相互作用方案。特别是，我们表明，对于强烈的最接近和下一期最新的邻居相互作用，只要初始移动的密度足够低，随机初始状态将定位。
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.
