Phase transitions in the Rényi entropies of a 2+1D large- N interacting vector model

We consider the reduced density matrix for a disk in the ground state of the interacting fixed points of the large-NO(N) vector model in 2+1 dimensions. Using the map to the free energy on H2×S1, we show that there is an instability in the Rényi entropies at n=1 in the N→∞ limit, indicating a phase transition at or near this Rényi parameter. We close with a discussion of the finite-N case.