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We propose the strongly tilted Bose-Hubbard model as a natural platform toexplore Hilbert-space fragmentation (HSF) and fracton dynamics intwo-dimensions, in a setup and regime readily accessible in optical latticeexperiments. Using a perturbative ansatz, we find HSF when the model is tunedto the resonant limit of on-site interaction and tilted potential. First, weinvestigate the quench dynamics of this system and observe numerically that therelaxation dynamics strongly depends on the chosen initial state -- one of thekey signature of HSF. Second, we identify fractonic excitations with restrictedmobility leading to anomalous transport properties. Specifically, we findexcitations that show one dimensional diffusion (z = 1/2) as well asexcitations that show subdiffusive behaviour in two dimensions (z = 3/4). Usinga cellular automaton, we analyze their dynamics and compare to an effectivehydrodynamic description.

Realization of Hilbert Space Fragmentation and Fracton Dynamics in 2D