On phase transitions in the Rényi entropies of 2+1-d large-N interacting vector models

Abstract

We consider the reduced density matrix for a disc in the ground state of the interacting fixed points of the large-N O(N) vector model in 2+1 dimensions. Using the map to the free energy on ${\mathbb{H}}_2\times S^1$, we show that there is an instability in the Rényi entropies at $n=1$, in the $N\to \infty$ limit, indicating a phase transition at or near this Rényi parameter. We close with a discussion of the finite-N case.

22 pages, v2: (a) references added; (b) further argument added that instability signals a second-order phase transition; (c) argument added that a phase transition at the Renyi parameter n = 1 does not necessarily prelude the use of the replica trick to compute the von Neumann entropy