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U(1) symmetry resolved entanglement in free 1+1 dimensional field theories via form factor bootstrap

Journal of High Energy Physics volume 2021, Article number: 197 (2021) Cite this article

A preprint version of the article is available at arXiv.

Abstract

We generalise the form factor bootstrap approach to integrable field theories with U(1) symmetry to derive matrix elements of composite branch-point twist fields associated with symmetry resolved entanglement entropies. The bootstrap equations are solved for the free massive Dirac and complex boson theories, which are the simplest theories with U(1) symmetry. We present the exact and complete solution for the bootstrap, including vacuum expectation values and form factors involving any type and arbitrarily number of particles. The non-trivial solutions are carefully cross-checked by performing various limits and by the application of the ∆-theorem. An alternative and compact determination of the novel form factors is also presented. Based on the form factors of the U(1) composite branch-point twist fields, we re-derive earlier results showing entanglement equipartition for an interval in the ground state of the two models.

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Authors and Affiliations

  1. SISSA and INFN Sezione di Trieste, via Bonomea 265, 34136, Trieste, Italy

    Dávid X. Horváth, Luca Capizzi & Pasquale Calabrese

  2. International Centre for Theoretical Physics (ICTP), Strada Costiera 11, 34151, Trieste, Italy

    Pasquale Calabrese

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  1. Dávid X. Horváth
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Horváth, D.X., Capizzi, L. & Calabrese, P. U(1) symmetry resolved entanglement in free 1+1 dimensional field theories via form factor bootstrap. J. High Energ. Phys. 2021, 197 (2021). https://doi.org/10.1007/JHEP05(2021)197

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Keywords

  • Field Theories in Lower Dimensions
  • Global Symmetries
  • Integrable Field
  • Theories