Entanglement entropy in the O(N) model

It is generally believed that in spatial dimension d>1, the leading contribution to the entanglement entropy S=−tr ρ_A log ρ_A scales as the area of the boundary of subsystem A. The coefficient of this “area law” is nonuniversal. However, in the neighborhood of a quantum critical point S is believed to possess subleading universal corrections. In the present work, we study the entanglement entropy in the quantum O(N) model in 1<d<3. We use an expansion in ϵ=3−d to evaluate (i) the universal geometric correction to S for an infinite cylinder divided along a circular boundary; (ii) the universal correction to S due to a finite correlation length. Both corrections are different at the Wilson-Fisher and Gaussian fixed points, and the ϵ→0 limit of the Wilson-Fisher fixed point is distinct from the Gaussian fixed point. In addition, we compute the correlation length correction to the Renyi entropy S_n=1/1−nlog tr ρ_Aⁿ in ϵ and large-N expansions. For N→∞, this correction generally scales as N² rather than the naively expected N. Moreover, the Renyi entropy has a phase transition as a function of n for d close to 3.