Journal of Statistical Physics

, Volume 130, Issue 1, pp 129–168 | Cite as

Form Factors of Branch-Point Twist Fields in Quantum Integrable Models and Entanglement Entropy

  • J. L. Cardy
  • O. A. Castro-AlvaredoEmail author
  • B. Doyon


In this paper we compute the leading correction to the bipartite entanglement entropy at large sub-system size, in integrable quantum field theories with diagonal scattering matrices. We find a remarkably universal result, depending only on the particle spectrum of the theory and not on the details of the scattering matrix. We employ the “replica trick” whereby the entropy is obtained as the derivative with respect to n of the trace of the nth power of the reduced density matrix of the sub-system, evaluated at n=1. The main novelty of our work is the introduction of a particular type of twist fields in quantum field theory that are naturally related to branch points in an n-sheeted Riemann surface. Their two-point function directly gives the scaling limit of the trace of the nth power of the reduced density matrix. Taking advantage of integrability, we use the expansion of this two-point function in terms of form factors of the twist fields, in order to evaluate it at large distances in the two-particle approximation. Although this is a well-known technique, the new geometry of the problem implies a modification of the form factor equations satisfied by standard local fields of integrable quantum field theory. We derive the new form factor equations and provide solutions, which we specialize both to the Ising and sinh-Gordon models.


Integrable quantum field theory Entanglement entropy Form factors Twist fields 


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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • J. L. Cardy
    • 2
    • 3
  • O. A. Castro-Alvaredo
    • 1
    Email author
  • B. Doyon
    • 3
  1. 1.Centre for Mathematical ScienceCity University LondonLondonUK
  2. 2.All Souls CollegeOxfordUK
  3. 3.Rudolf Peierls Centre for Theoretical PhysicsOxford UniversityOxfordUK

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