Hilbert space fragmentation and hydrodynamics in two-dimensional systems

Higher-moment conservation in lattice systems can lead to Hilbert space fragmentation and anomalous transport. While many physical insights can be already drawn from one-dimensional systems, we uncover a richer structure in the two-dimensional case. We find that different components of the quadrupole moment can be conserved and, in the weakly fragmented regime, lead to potentially different hydrodynamic descriptions which in all cases results in subdiffusion. To validate these concepts, we numerically investigate the stochastic evolution of blocked cellular automata with higher-moment conservation.