Entanglement entropy along a massless renormalisation flow: the tricritical to critical Ising crossover

TL;DR

This paper analytically investigates the entanglement entropy along a massless renormalisation flow from tricritical to critical Ising models, revealing how different particle interactions contribute to the entropy's structure.

Contribution

It introduces a bootstrap approach to compute twist field form factors in a massless flow, connecting integrable field theories with the entanglement entropy analysis.

Findings

Form factor expansion separates infrared and ultraviolet contributions.

Derived analytical expressions for composite twist fields related to symmetry resolution.

Connected the form factors to the roaming limit of sinh-Gordon theory.

Abstract

We study the R\'enyi entanglement entropies along the massless renormalisation group flow that connects the tricritical and critical Ising field theories. Similarly to the massive integrable field theories, we derive a set of bootstrap equations, from which we can analytically calculate the twist field form factors in a recursive way. Additionally, we also obtain them as a non-trivial roaming limit of the sinh-Gordon theory. Then the R\'enyi entanglement entropies are obtained as expansions in terms of the form factors of these branch point twist fields. We find that the form factor expansion of the entanglement entropy along the flow organises in two different kind of terms. Those that couple particles with the same chirality, and reproduce the entropy of the infrared Ising theory, and those that couple particles with different chirality, which provide the ultraviolet contributions. The massless flow under study possesses a global $\mathbb{Z}_2$ spin-flip symmetry. We further consider the composite twist fields associated to this group, which enter in the study of the symmetry resolution of the entanglement. We derive analytical expressions for their form factors both from the bootstrap equations and from the roaming limit of the sinh-Gordon theory.