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

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 Rényi 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.

35 pages; 9 figures; 3 tables

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• Post-Quantum Quench Growth of Renyi Entropies in Low Dimensional Continuum Bosonic Systems
• Robust effective ground state in a nonintegrable Floquet quantum circuit
• A study of integrable form factors in massless relativistic AdS_3
• Quantum quenches from an excited state
• Entanglement entropy along a massless renormalisation flow: the tricritical to critical Ising crossover
• Exact mapping from the $(3+1)$-dimensional Skyrme model to the $(1+1)$-dimensional sine-Gordon theory and some applications
• Entanglement of Stationary States in the Presence of Unstable Quasiparticles