Checkerboard phase dynamics in the parallel update Manna model

We find a novel checkerboard phase of a parallel update Manna sandpile model with a conserved number of particles on square lattice. At high densities above the absorbing-active transition, instead of seeing a randomly diffusive active phase with the conventional random sequential update, the system spontaneously separates into two sets of alternating checkerboard phases when following the parallel update rule. We explore a variety of the checkerboard phase phenomena including the Model A-like coarsening dynamics, density-dependent domain wall thickness, and nucleation-like behavior at higher density. A mean-field description is also proposed to capture the properties of this discrete checkerboard Manna model.