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

In this paper, we apply the form factor bootstrap approach to branch point twist fields in the $q$-state Potts model for $qleq 3$. 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 $qleq 3$ the standard Renyi 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 $qleq 3$ 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.