We numerically determine subleading scaling terms in the ground-state entanglement entropy of several two-dimensional (2D) gapless systems, including a Heisenberg model with Néel order, a free Dirac fermion in the $\pi$-flux phase, and the nearest-neighbor resonating-valence-bond wave function. 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 on 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.

• Received 1 January 2012

DOI:https://doi.org/10.1103/PhysRevB.85.165121