Entanglement subvolume law for 2D frustration-free spin systems

Let H be a frustration-free Hamiltonian describing a 2D grid of spins with local interactions, and assume it has a unique ground state  with a local spectral gap.  We show that for any bi-partition of the grid into a  region A and its complement, the entanglement entropy in the ground state is upper bounded by O(∂A^5/3), where ∂A is the boundary of A. This represents the first subvolume bound on entanglement in frustration-free 2D systems under such general conditions.