We show that the combination of charge and dipole conservation—characteristic of fracton systems—leads to an extensive fragmentation of the Hilbert space, which in turn can lead to a breakdown of thermalization. As a concrete example, we investigate the out-of-equilibrium dynamics of one-dimensional spin-1 models that conserve charge (total $S^z$) and its associated dipole moment. First, we consider a minimal model including only three-site terms and find that the infinite temperature auto-correlation saturates to a finite value—showcasing non-thermal behavior. The absence of thermalization is identified as a consequence of the of the Hilbert space into exponentially many invariant subspaces in the local $S^z$ basis, arising from the interplay of dipole conservation and local interactions. Second, we extend the model by including four-site terms and find that this perturbation leads to a : the system still has exponentially many invariant subspaces, but they are no longer sufficient to avoid thermalization for typical initial states. More generally, for any finite range of interactions, the system still exhibits non-thermal eigenstates appearing throughout the entire spectrum. We compare our results to charge and dipole moment conserving random unitary circuit models for which we reach identical conclusions.

中文翻译：

---

保偶极子哈密顿量中希尔伯特空间碎裂引起的遍历性破坏

我们表明，电荷和偶极子守恒的结合（分数系统的特征）导致希尔伯特空间的广泛破碎，进而导致热分解。作为一个具体的例子，我们研究了节省电荷的一维spin-1模型的不平衡动力学（总${\mathrm{小号}}^{ž}$）及其相关的偶极矩。首先，我们考虑一个仅包含三个位置项的最小模型，并发现无限温度自相关饱和到一个有限值，这表明了非热行为。由于希尔伯特空间进入局部指数成许多不变子空间的结果，确定没有热化${\mathrm{小号}}^{ž}$偶极守恒与局部相互作用的相互作用 其次，我们通过包括四个位点的项来扩展模型，发现这种扰动导致：系统仍然具有指数级的不变子空间，但是它们不再足以避免典型初始状态的热化。更一般地，对于任何有限范围的相互作用，系统仍然表现出遍及整个光谱的非热本征态。我们将结果与电荷和偶极矩守恒随机unit电路模型进行比较，得出相同的结论。