Multipole conservation laws and subdiffusion in any dimension

Abstract: Subdiffusion is a generic feature of chaotic many-body dynamics with multipole conservation laws and subsystem symmetries. We numerically study this subdiffusive dynamics, using quantum automaton random unitary circuits, in a broad range of models including one dimensional models with dipole and quadrupole conservation, two dimensional models with dipole conservation, and two dimensional models with subsystem symmetry on the triangular lattice. Our results are in complete agreement with recent hydrodynamic predictions for such theories.