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We consider the ground state of the one-dimensional quantum Ising model withtransverse field $h_x$ in one dimension depending on the site $x \in \mathbb Z$in a finite volume $\Lambda_{m}:=\{-m,-m+1,\ldots,m+L\}\ $. We make suitableassumptions on the regions where the field is small and prove that if the fieldis sufficiently large on the complementary set, then the entanglement of theinterval $\Lambda_{0}:=\left\{ 0,..,L\right\} $ relative to its complement$\Lambda_{m}\backslash\Lambda_{0}$ is bounded uniformly in $m$ and $L$. Theresult applies in particular to periodic transverse fields. The bound isestablished by means of a suitable cluster expansion.

Uniform bound of the entanglement for the ground state of the one-dimensional quantum Ising model with non-homogeneous transverse field