Branch Point Twist Field Form Factors in the sine-Gordon Model I: Breather Fusion and Entanglement Dynamics

TL;DR

This paper computes form factors of the branch point twist field in the sine-Gordon model, analyzing entanglement dynamics after a quench, revealing undamped oscillations in entropies due to breather interactions.

Contribution

It introduces a method to compute breather form factors via fusion and applies this to study entanglement oscillations post-quench in the sine-Gordon model.

Findings

Entanglement entropies oscillate undamped with frequencies related to breather masses.

Form factors of heavier breathers derived from lighter ones using fusion.

Oscillation amplitudes linked to breather one-particle form factors.

Abstract

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 programme. In this paper we compute the 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 posesses 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 R\'enyi 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.