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In this paper we compute the leading correction to the bipartite entanglemententropy at large sub-system size, in integrable quantum field theories withdiagonal scattering matrices. We find a remarkably universal result, dependingonly on the particle spectrum of the theory and not on the details of thescattering matrix. We employ the "replica trick" whereby the entropy isobtained as the derivative with respect to n of the trace of the n-th power ofthe reduced density matrix of the sub-system, evaluated at n=1. The mainnovelty of our work is the introduction of a particular type of twist fields inquantum field theory that are naturally related to branch points in ann-sheeted Riemann surface. Their two-point function directly gives the scalinglimit of the trace of the n-th power of the reduced density matrix. Takingadvantage of integrability, we use the expansion of this two-point function interms of form factors of the twist fields, in order to evaluate it at largedistances in the two-particle approximation. Although this is a well-knowntechnique, the new geometry of the problem implies a modification of the formfactor equations satisfied by standard local fields of integrable quantum fieldtheory. We derive the new form factor equations and provide solutions, which wespecialize both to the Ising and sinh-Gordon models.

Form factors of branch-point twist fields in quantum integrable models and entanglement entropy