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

TL;DR

This paper extends the form factor bootstrap method to compute symmetry-resolved entanglement in free 1+1D integrable field theories with U(1) symmetry, providing exact solutions and confirming entanglement equipartition.

Contribution

It develops a comprehensive bootstrap approach for U(1) symmetry in integrable models and derives exact form factors for composite twist fields.

Findings

Exact form factors for U(1) twist fields in free Dirac and boson theories.

Confirmation of entanglement equipartition in these models.

Cross-checked solutions via limits and the Delta-theorem.

Abstract

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 Delta-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.