In recent years the characterization of many-body ground states via the entanglement of their wave-function has attracted a lot of attention. One useful measure of entanglement is provided by the entanglement entropy S.
The interest in this quantity has been sparked, in part, by the result that at one dimensional quantum critical points (QCPs) S scales logarithmically with the subsystem size with a universal coefficient related to the central charge of the conformal field theory describing the QCP. On the other hand, in spatial dimension d > 1 the leading contribution to the entanglement entropy scales as the area of the boundary of the subsystem. The coefficient of this "area law" is non-universal. However, in the neighbourhood of a QCP, S is believed to possess subleading universal corrections. In this talk, I will present the first field-theoretic study of entanglement entropy in dimension d > 1 at a stable interacting QCP - the quantum O(N) model. Our results confirm the presence of universal corrections to the entanglement entropy and exhibit a number of surprises such as different epsilon -> 0 limits of the Wilson-Fisher and Gaussian fixed points, violation of large N counting and subtle dependence on replica index.