Unusual corrections to scaling in entanglement entropy

Abstract

We present a general theory of the corrections to the asymptotic behaviour of the Rényi entropiesSA(n) = (1 − n) − 1logTrρAn which measure the entanglement of an interval A of length with the rest of an infinite one-dimensional system, in the casewhen this is described by a conformal field theory of central chargec. These can be due to bulk irrelevant operators of scaling dimensionx > 2, in which case the leading corrections are of the expected form for values of n closeto 1. However, for n > x/(x − 2) corrections of the form and arise and dominate the conventional terms. We also point out that the last type of corrections can also occurwith x less than 2. They arise from relevant operators induced by the conical spacetimesingularities necessary to describe the reduced density matrix. These agree with recentanalytic and numerical results for quantum spin chains. We also compute the effect ofmarginally irrelevant bulk operators, which give a correction , with a universal amplitude. We present analogous results for the case when the intervallies at the end of a semi-infinite system.