  Ground states of quantum many-body systems are both entangled and possess a
kind of quantum complexity as their preparation requires universal resources
that go beyond the Clifford group and stabilizer states. These resources -
sometimes described as magic - are also the crucial ingredient for quantum
advantage. We study the behavior of the stabilizer R\'enyi entropy in the
integrable transverse field Ising spin chain. We show that the locality of
interactions results in a localized stabilizer R\'enyi entropy in the gapped
phase thus making this quantity computable in terms of local quantities in the
gapped phase, while measurements involving $L$ spins are necessary at the
critical point to obtain an error scaling with $O(L^{-1})$.
