Branch point twist field form factors in the sine-Gordon model I: Breather fusion and entanglement dynamics

The quantum sine-Gordon model is the simplest massive interacting integrable quantum field theory whose two-particle scattering matrix is generally non-diagonal. As such, it is a model that has been extensively studied, especially in the context of the bootstrap program. In this paper we compute low particle-number form factors of a special local field known as the branch point twist field, whose correlation functions are building blocks for measures of entanglement. We consider the attractive regime where the theory possesses a particle spectrum consisting of a soliton, an antisoliton (of opposite U(1) charges) and several (neutral) breathers. In the breather sector we exploit the fusion procedure to compute form factors of heavier breathers from those of lighter ones. We apply our results to the study of the entanglement dynamics after a small mass quench and for short times. We show that in the presence of two or more breathers the von Neumann and Renyi entropies display undamped oscillations in time, whose frequencies are proportional to the even breather masses and whose amplitudes are proportional to the breather's one-particle form factor.

Automated summary

The quantum sine-Gordon model is studied in this paper, focusing on the computation of low particle-number form factors and the correlation functions of the branch point twist field for measuring entanglement. The theory's attractive regime with solitons, antisolitons, and breathers is considered, with form factors computed using the fusion procedure. The study shows undamped oscillations in von Neumann and Renyi entropies over time, with frequencies and amplitudes related to the breather masses and form factors respectively.