Breaking the area law in a solvable 2D spin model

We introduce a solvable lattice model of spins in D=2 spatial dimensions for which the ground states have an entanglement entropy which scales as S ∼ L^D-1 log(L) and thus break the area law. Whereas this breaking of the area law is well-established for free fermions, proving that it can exist for the ground states of a local spin Hamiltonian in D>1, it is to the best of our knowledge, unprecedented. The model describes a triangular lattice Ising antiferromagnet for which each domain wall is decorated by a gapless spin chain. The macroscopic degeneracy between antiferromagnetic configurations is only split by the Casimir effect of each decorating spin chain, i.e., the finite-size corrections to their ground state energy. Remarkably, we found a decorating spin chain for which the Casimir energy is positive, which makes it favorable for domain walls to coalesce into a single, macroscopically large 1D "snake'' lacing the whole 2D system. Since the snake is decorated by a gapless spin chain, one finds naturally an L log(L) contribution to the entanglement entropy. Using a combination of conformal field theory and Monte Carlo techniques, we calculated various properties of this "snake'' phase, including two-point functions and entanglement.