Universal corner entanglement of Dirac fermions and gapless bosons from the continuum to the lattice

A quantum critical (QC) fluid exhibits universal subleading corrections to the area law of its entanglement entropies. In two dimensions, when the partition involves a corner of angle theta, the subleading term is logarithmic with coefficient a(alpha)(theta) for the alpha-Renyi entropy. In the smooth limit theta -> pi, a(1)(theta) yields the central charge of the stress tensor when the QC point is described by a conformal field theory (CFT). For general Renyi indices and angles, a(alpha)(theta) is richer and few general results exist. We study a(alpha)(theta) focusing on two benchmark CFTs, the free Dirac fermion and boson. We perform numerical lattice calculations to obtain high precision results in 0, alpha regimes hitherto unexplored. We derive field theory estimates for a(alpha)(theta), including exact results, and demonstrate an excellent quantitative match with our numerical calculations. We also develop and test strong lower bounds, which apply to both free and interacting QC systems. Finally, we comment on the near collapse of a(alpha)(theta) for various theories, including interacting O(N) models.