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 q <= 3. For q = 3 this is an integrable interacting quantum field theory with an internal discrete Z(3) symmetry and therefore provides an ideal starting point for the investigation of the symmetry resolved entanglement entropies. However, more generally, for q <= 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 q <= 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.

Automated summary

In this paper, the form factor bootstrap approach is applied to branch point twist fields in the q-state Potts model for q <= 3. The model is an integrable interacting quantum field theory with an internal discrete Z(3) symmetry for q = 3, making it an ideal starting point for investigating symmetry resolved entanglement entropies. Furthermore, the standard Renyi and entanglement entropies can also be accessed through the bootstrap program for q <= 3. Form factor solutions are presented for both the standard branch point twist field with q <= 3 and the composite branch point twist field with q = 3, with the solutions carefully checked via the Delta-sum rule. The leading finite-size corrections to the entanglement entropy and entanglement equipartition for a single interval in the ground state are computed using the analytical predictions.