# Bounded entanglement entropy in the quantum Ising model

## TL;DR

This paper provides a rigorous proof that the entanglement entropy remains bounded in the ground state of the one-dimensional quantum Ising model with a strong transverse field, using a geometrical approach and classical probability models.

## Contribution

It introduces a robust geometrical proof technique for entanglement entropy bounds, extending to disordered systems, based on a transformation to the continuum random-cluster model.

## Key findings

- Entanglement entropy is bounded in the quantum Ising model with strong transverse field.
- The proof employs a geometrical approach and classical probability models.
- Method applies to certain disordered quantum systems.

## Abstract

A rigorous proof is presented of the boundedness of the entanglement entropy of a block of spins for the ground state of the one-dimensional quantum Ising model with sufficiently strong transverse field. This is proved by a refinement of the arguments in the earlier work by the same authors (J. Statist. Phys. 131 (2008) 305-339). The proof is geometrical, and utilises a transformation to a model of classical probability called the continuum random-cluster model. Our method of proof is fairly robust, and applies also to certain disordered systems.