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.