Entanglement scaling in two-dimensional gapless systems

We numerically determine subleading scaling terms in the ground-state entanglement entropy of several two-dimensional (2D) gapless systems, including a Heisenberg model with N\'eel order, a free Dirac fermion in the {\pi}-flux phase, and the nearest-neighbor resonating-valence-bond wavefunction. For these models, we show that the entanglement entropy between cylindrical regions of length x and L - x, extending around a torus of length L, depends upon the dimensionless ratio x/L. This can be well-approximated on finite-size lattices by a function ln(sin({\pi}x/L)), akin to the familiar chord-length dependence in one dimension. We provide evidence, however, that the precise form of this bulk-dependent contribution is a more general function in the 2D thermodynamic limit.