  We consider the partial transpose of the spin reduced density matrix of two
disjoint blocks in spin chains admitting a representation in terms of free
fermions, such as XY chains. We exploit the solution of the model in terms of
Majorana fermions and show that such partial transpose in the spin variables is
a linear combination of four Gaussian fermionic operators. This representation
allows to explicitly construct and evaluate the integer moments of the partial
transpose. We numerically study critical XX and Ising chains and we show that
the asymptotic results for large blocks agree with conformal field theory
predictions if corrections to the scaling are properly taken into account.
