Observation of Hilbert-space fragmentation and fractonic excitations in two-dimensional Hubbard systems

Hilbert-space fragmentation characterises a new class of constrained quantum systems and can influence their ergodicity. Here we show how Hubbard models can be used as a natural platform to explore Hilbert-space fragmentation and fracton dynamics in two-dimensions, in a setup and regime readily accessible in optical lattice experiments. We investigate the quench dynamics of this system and observe experimentally 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. Our results mark the first observation of HSF beyond one dimension, as well as the concomitant direct observation of fractons, and pave the way for in-depth studies of microscopic transport phenomena in constrained systems.