We propose the strongly tilted Bose-Hubbard model as a natural platform to explore Hilbert-space fragmentation (HSF) and fracton dynamics in two dimensions in a setup and regime readily accessible in optical lattice experiments. Using a perturbative ansatz, we find HSF when the model is tuned to the resonant limit of on-site interaction and tilted potential. First, we investigate the quench dynamics of this system and observe numerically that the relaxation dynamics strongly depends on the chosen initial state—one of the key signatures of HSF. Second, we identify fractonic excitations with restricted mobility leading to anomalous transport properties. Specifically, we find excitations that show one-dimensional diffusion (𝑧=1/2) as well as excitations that show subdiffusive behavior in two dimensions (𝑧=3/4). Using a cellular automaton, we analyze their dynamics and compare it to an effective hydrodynamic description.

中文翻译：

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希尔伯特空间碎片化和二维弗克顿动力学的实现


我们提出了强烈倾斜的 Bose-Hubbard 模型作为一个自然平台，在二维中设置和状态中探索希尔伯特空间碎片 （HSF） 和分形动力学，该设置和机制在光晶格实验中很容易获得。使用扰动拟设，当模型被调整到现场相互作用和倾斜电位的谐振极限时，我们发现 HSF。首先，我们研究了该系统的猝灭动力学，并从数值上观察到弛豫动力学在很大程度上取决于所选的初始状态——HSF 的关键特征之一。其次，我们确定了迁移率受限的分形激发，导致异常的传输特性。具体来说，我们发现了显示一维扩散的激发 （z=1/2） 以及在二维中显示亚扩散行为的激发 （z=3/4）。使用元胞自动机，我们分析了它们的动力学，并将其与有效的流体动力学描述进行了比较。