Entanglement Entropy Scaling of 2D Critical Wave Functions

While CFT calculations have revealed a variety of universal predictions for the entanglement spectrum of critical 1+1D field theories, much less is known about higher-dimensional systems. CFT methods can be extended to a class of 2+1D theories characterized by a $z = 2$ critical point, the so-called Rokhsar-Kivelson wave functions. The entanglement entropy of RK-type critical wave functions contains a universal logarithmic contribution $\gamma \log( L )$ for some geometries arising from a trace anomaly in the corresponding CFT. We first re-examine the free boson, where the existence of order-unity contributions that depend on the boson compactification radius has been discussed in several recent papers (Hsu et al., St\'ephan et al., Oshikawa). We find analytically and numerically that the logarithmic contribution exists with the coefficient predicted by Fradkin and Moore and is independent of the compactification. However, it appears that their conjecture that general CFTs show the same dependence of $\gamma$ on central charge as the free boson is incorrect. We present arguments and numerical evidence for this conclusion in $c = 1/2$ and $c=1$ lattice models.