Universal corrections to scaling for block entanglement in spin-1/2 XX chains

We consider the Renyi entropies S(n)(l) in the one-dimensional spin1/ 2 Heisenberg XX chain in a magnetic field. The case n = 1 corresponds to the von Neumann 'entanglement' entropy. Using a combination of methods based on the generalized Fisher Hartwig conjecture and a recurrence relation connected to the Painleve e VI differential equation we obtain the asymptotic behaviour, accurate to order O(l(-3)), of the Renyi entropies S(n)(l) for large block lengths l. For n = 1, 2, 3, 10 this constitutes the 3, 6, 10, 48 leading terms respectively. The o(1) contributions are found to exhibit a rich structure of oscillatory behaviour, which we analyse in some detail both for finite n and in the limit n ->infinity.