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

Abstract

We consider the ground state of the one-dimensional quantum Ising model with transverse field $h_x$ in one dimension depending on the site $x\in \mathbb{Z}$ in a finite volume ${\Lambda }_m:=\{-m,-m+1,\dots ,m+L\}$. We make suitable assumptions on the regions where the field is small and prove that if the field is sufficiently large on the complementary set, then the entanglement of the interval ${\Lambda }_0:=\left\{0,..,L\right\}$ relative to its complement ${\Lambda }_m\backslash {\Lambda }_0$ is bounded uniformly in $m$ and $L$. The result applies in particular to periodic transverse fields. The bound is established by means of a suitable cluster expansion.

arXiv comment13 pages