Anshu, AnuragArad, ItaiGosset, David2024-04-172022-04-15Anshu, Anurag, Itai Arad, David Gosset. "Entanglement Subvolume Law for 2D Frustration-Free Spin Systems." Commun. Math. Phys. 393, no. 2 (2022): 955-988. DOI: 10.1007/s00220-022-04381-20010-36161432-0916https://nrs.harvard.edu/URN-3:HUL.INSTREPOS:37378338Let H be a frustration-free Hamiltonian describing a 2D grid of qudits with local interactions, a unique ground state, and local spectral gap lower bounded by a positive constant. For any bipartition defined by a vertical cut of length L running from top to bottom of the grid, we prove that the corresponding entanglement entropy of the ground state of H is upper bounded by Õ (L5/3). For the special case of a 1D chain, our result provides a new area law which improves upon prior work, in terms of the scaling with qudit dimension and spectral gap. In addition, for any bipartition of the grid into a rectangular region A and its complement, we show that the entanglement entropy is upper bounded as Õ (|∂A|5/3) where ∂A is the boundary of A. This represents the first subvolume bound on entanglement in frustration-free 2D systems. In contrast with previous work, our bounds depend on the local (rather than global) spectral gap of the Hamiltonian. We prove our results using a known method which bounds the entanglement entropy of the ground state in terms of certain properties of an approximate ground state projector (AGSP). To this end, we construct a new AGSP which is based on a robust polynomial approximation of the AND function and we show that it achieves an improved trade-off between approximation error and entanglement.en-USMathematical PhysicsStatistical and Nonlinear PhysicsJournal Article2024-04-1710.1007/s00220-022-04381-2