LAUSR

We consider the ground state of the quantum Ising model with transverse field h in one dimension in a finite volume $$\begin{aligned} \Lambda {_{m}:=\{-m,-m+1,\ldots ,m+L\}.} \end{aligned}$$ Λ m : = { - m , - m + 1 , … , m + L } . For h sufficiently large we prove a bound for the entanglement of the interval $$\Lambda _{0}:=\left\{ 0,\ldots ,L\right\} $$ Λ 0 : = 0 , … , L relative to its complement $$\Lambda _{m}\backslash \Lambda _{0}$$ Λ m \ Λ 0 which is uniform in m and L . The bound is established by means of a suitable cluster expansion.