Bi-partite entanglement entropy in massive 1+1-dimensional quantum field theories

TL;DR

This paper reviews a new method combining the replica trick and form factors to compute bi-partite entanglement entropy in massive 1+1-dimensional quantum field theories, especially integrable models, providing exact infrared and ultraviolet results.

Contribution

It introduces a novel approach using branch-point twist fields and form factors to analytically calculate entanglement entropy in massive quantum field theories, including non-integrable cases.

Findings

Exact infrared behavior of entanglement entropy obtained.

Ultraviolet behavior analyzed for various models.

Method applicable to theories with boundaries and backscattering.

Abstract

This manuscript is a review of the main results obtained in a series of papers involving the present authors and their collaborator J.L. Cardy over the last two years. In our work we have developed and applied a new approach for the computation of the bi-partite entanglement entropy in massive 1+1-dimensional quantum field theories. In most of our work we have considered these theories to be also integrable. Our approach combines two main ingredients: the "replica trick" and form factors for integrable models and more generally for massive quantum field theory. Our basic idea for combining fruitfully these two ingredients is that of the branch-point twist field. By the replica trick we obtained an alternative way of expressing the entanglement entropy as a function of the correlation functions of branch-point twist fields. On the other hand, a generalisation of the form factor program has allowed us to study, and in integrable cases to obtain exact expressions for, form factors of such twist fields. By the usual decomposition of correlation functions in an infinite series involving form factors, we obtained exact results for the infrared behaviours of the bi-partite entanglement entropy, and studied both its infrared and ultraviolet behaviours for different kinds of models: with and without boundaries and backscattering, at and out of integrability.