Realization of Hilbert Space Fragmentation and Fracton Dynamics in Two Dimensions

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.