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.

中文翻译：

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正弦-戈登模型中的分支点扭曲场形状因子 I：呼吸器融合和纠缠动力学

量子正弦-戈登模型是最简单的大规模相互作用可积量子场论，其二粒子散射矩阵通常是非对角线的。因此，它是一个被广泛研究的模型，特别是在引导程序的背景下。在本文中，我们计算称为分支点扭曲场的特殊局部场的形状因子，其相关函数是纠缠测量的构建块。我们考虑有吸引力的机制，其中理论提出了一个由孤子、反孤子（具有相反的 $U(1)$ 电荷）和几个（中性）呼吸器组成的粒子谱。在呼吸器部分，我们利用融合程序从较轻的呼吸器计算较重的呼吸器的形状因子。我们将我们的结果应用于小质量猝灭和短时间后的纠缠动力学研究。我们表明，在存在两个或更多呼吸器的情况下，von Neumann 和 R\'enyi 熵随时间显示无阻尼振荡，其频率与均匀呼吸器质量成正比，其振幅与呼吸器的单粒子形状因子成正比。