Boundedness of entanglement entropy for the ground state of the one-dimensional quantum Ising model with random transverse field at large disorder

We consider the ground state of the one-dimensional quantum Ising model with transverse field hx in one dimension depending on the site x∈Z in a finite volume. We assume hx = λξx, where (ξx),x∈Z is a family of strictly positive i.i.d. random variables with a positive density at 0 satisfying the condition. E(ξ0−δ)<∞ for some δ > 0 and λ > 0 is the disorder parameter. We prove that if λ is sufficiently large, the entanglement entropy of the ground state has a stochastic bound uniform with respect to the volume.