Bi-partite entanglement entropy in massive QFT with a boundary: the Ising model

TL;DR

This paper derives an exact series expression for the bi-partite entanglement entropy in the quantum Ising model with a boundary, extending previous integrable QFT results and connecting boundary entropy to entanglement measures.

Contribution

It provides a universal and exact formula for boundary entanglement entropy in the Ising model, generalizing form factor methods to boundary quantum field theories.

Findings

Derived an infinite-series expression for entanglement entropy

Isolated boundary entropy contribution in a universal way

Validated results through high-precision consistency checks

Abstract

In this paper we give an exact infinite-series expression for the bi-partite entanglement entropy of the quantum Ising model both with a boundary magnetic field and in infinite volume. This generalizes and extends previous results involving the present authors for the bi-partite entanglement entropy of integrable quantum field theories, which exploited the generalization of the form factor program to branch-point twist fields. In the boundary case, we isolate in a universal way the part of the entanglement entropy which is related to the boundary entropy introduced by Affleck and Ludwig, and explain how this relation should hold in more general QFT models. We provide several consistency checks for the validity of our form factor results, notably, the identification of the leading ultraviolet behaviour both of the entanglement entropy and of the two-point function of twist fields in the bulk theory, to a great degree of precision by including up to 500 form factor contributions.