U(1) symmetry resolved entanglement in free 1+1 dimensional field theories via form factor bootstrap

We generalise the form factor bootstrap approach to integrable field theories with U(1) symmetry to derive matrix elements of composite branch-point twist fields associated with symmetry resolved entanglement entropies. The bootstrap equations are solved for the free massive Dirac and complex boson theories, which are the simplest theories with U(1) symmetry. We present the exact and complete solution for the bootstrap, including vacuum expectation values and form factors involving any type and arbitrarily number of particles. The non-trivial solutions are carefully cross-checked by performing various limits and by the application of the -theorem. An alternative and compact determination of the novel form factors is also presented. Based on the form factors of the U(1) composite branch-point twist fields, we re-derive earlier results showing entanglement equipartition for an interval in the ground state of the two models.

Automated summary

In this study, the form factor bootstrap approach is extended to integrable field theories with U(1) symmetry to derive matrix elements of composite branch-point twist fields associated with symmetry resolved entanglement entropies. The exact and complete solution for the bootstrap equations is presented for the free massive Dirac and complex boson theories, including vacuum expectation values and form factors involving any type and arbitrarily number of particles. The novel form factors of the U(1) composite branch-point twist fields allow for the re-derivation of earlier results showing entanglement equipartition for an interval in the ground state of the two models.