Realization of Hilbert Space Fragmentation and Fracton Dynamics in 2D

Understand

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 signature of HSF.
• Second, we identify fractonic excitations with restricted mobility leading to anomalous transport properties.