Entanglement of the $3$-State Potts Model via Form Factor Bootstrap: Total and Symmetry Resolved Entropies

TL;DR

This paper uses the form factor bootstrap method to analyze entanglement entropies in the $q$-state Potts model for $q\, extless= 3$, providing new solutions for standard and symmetry-resolved entropies and calculating finite-size effects.

Contribution

It introduces form factor solutions for both standard and symmetry-resolved branch point twist fields in the $q$-state Potts model with $q\, extless= 3$, advancing the bootstrap approach for entanglement analysis.

Findings

Derived form factor solutions for $q\, extless= 3$ Potts model.

Computed finite-size corrections to entanglement entropy.

Analyzed symmetry resolution and entanglement equipartition.

Abstract

In this paper, we apply the form factor bootstrap approach to branch point twist fields in the $q$-state Potts model for $q\leq 3$. For $q=3$ this is an integrable interacting quantum field theory with an internal discrete $\mathbb{Z}_3$ symmetry and therefore provides an ideal starting point for the investigation of the symmetry resolved entanglement entropies. However, more generally, for $q\leq 3$ the standard R\'enyi and entanglement entropies are also accessible through the bootstrap programme. In our work we present form factor solutions both for the standard branch point twist field with $q\leq 3$ and for the composite (or symmetry resolved) branch point twist field with $q=3$. In both cases, the form factor equations are solved for two particles and the solutions are carefully checked via the $\Delta$-sum rule. Using our analytic predictions, we compute the leading finite-size corrections to the entanglement entropy and entanglement equipartition for a single interval in the ground state.