Symmetry resolved entanglement in integrable field theories via form factor bootstrap

TL;DR

This paper develops a form factor bootstrap method to compute symmetry-resolved entanglement entropies in integrable quantum field theories, providing explicit results for models like the Ising and sinh-Gordon theories.

Contribution

It introduces a novel bootstrap approach for symmetry-resolved entanglement in integrable models and computes explicit universal functions for the Ising model.

Findings

Entanglement equipartition is generally expected in these models.

The first subleading correction breaking equipartition is identified.

Complete computation of symmetry-resolved von Neumann entropy for the Ising model is provided.

Abstract

We consider the form factor bootstrap approach of integrable field theories to derive matrix elements of composite branch-point twist fields associated with symmetry resolved entanglement entropies. The bootstrap equations are determined in an intuitive way and their solution is presented for the massive Ising field theory and for the genuinely interacting sinh-Gordon model, both possessing a $\mathbb{Z}_{2}$ symmetry. The solutions are carefully cross-checked by performing various limits and by the application of the $\Delta$-theorem. The issue of symmetry resolution for discrete symmetries is also discussed. We show that entanglement equipartition is generically expected and we identify the first subleading term (in the UV cutoff) breaking it. We also present the complete computation of the symmetry resolved von Neumann entropy for an interval in the ground state of the paramagnetic phase of the Ising model. In particular, we compute the universal functions entering in the charged and symmetry resolved entanglement.