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

by Olalla A. Castro-Alvaredo, David X. Horvath

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Submission summary

Authors (as registered SciPost users): David Horvath
Submission information
Preprint Link:  (pdf)
Date accepted: 2021-05-31
Date submitted: 2021-05-22 12:05
Submitted by: Horvath, David
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • High-Energy Physics - Theory
Approach: Theoretical


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.

Published as SciPost Phys. 10, 132 (2021)

List of changes

We have implemented the following changes:

We have changed 'programme' to 'program'.

We have specified that we consider in this work only low particle number form factors by writing “low particle-number” in the abstract and at the beginning of the conclusion.

We have slightly reworded paragraph 2 in the introduction to stress that the approach of Smirnov and Babujian et al. can be regarded as the same one using different Hilbert spaces.

We have explicitly mentioned Smirnov works in the introduction stressing that the fusion procedure was already applied in his works.

We have added the references: H. Babujian and M. Karowski, Sine-Gordon breather form factors and quantum field equations, J.Phys.A, 35, (2002), 9081-9104.) and V. Brazhnikov and S. Lukyanov, Angular quantization and form factors in massive integrable models , Nucl. Phys. B, 512, 3, (1998), 616-636).

We have proved our formulas (131) and (140, in the updated version) in Appendix D using Gamma-function identities rather than quantum di-logarithms.

We have cited the papers G. Delfino, Phys. Lett. B 450 (1999) 196 and G. Delfino, P. Grinza, NPB 682 (2004) 521 in the second paragraph of the introduction.

A typo on page 19 just above the paragraph “We demonstrate …”: the regime of damped oscillations is ξ>1/2 (not ξ<1/2) has been noted and corrected.

We have added to more more papers to our references:
[52] K. Hodsagi, M. Kormos, and G. Takacs, Quench dynamics of the Ising field theory in a magnetic field, SciPost Phys. 5(027) (2018).
[53]  K. Hodsagi, M. Kormos, and G. Takacs, Perturbative post-quench overlaps in Quantum Field Theory, JHEP 2019(47) (2019).

Finally, we have found several instances in the introduction and in the conclusion, where we originally wrote 'where' instead of 'were'. These typos have been corrected.

Reports on this Submission

Anonymous Report 2 on 2021-5-24 (Invited Report)


The paper has been updated and can be published.

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

Anonymous Report 1 on 2021-5-23 (Invited Report)


I have no more comments and recommend the paper for publication.

  • validity: ok
  • significance: good
  • originality: ok
  • clarity: high
  • formatting: excellent
  • grammar: excellent

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