  We study the Renyi entanglement entropies of two disjoint intervals in XY
chains. We exploit the exact solution of the model in terms of free Majorana
fermions and we show how to construct the reduced density matrix in the spin
variables by taking properly into account the Jordan-Wigner string between the
two blocks. From this we can evaluate any Renyi entropy of finite integer
order. We study in details critical XX and Ising chains and we show that the
asymptotic results for large blocks agree with recent conformal field theory
predictions if corrections to the scaling are included in the analysis
correctly. We also report results in the gapped phase and after a quantum
quench.
