Letters in Mathematical Physics

, Volume 109, Issue 3, pp 675–698 | Cite as

New exact results on density matrix for XXX spin chain

  • T. Miwa
  • F. SmirnovEmail author


Using the fermionic basis, we obtain the expectation values of all \({\mathfrak {sl}}_{2}\)-invariant and C-invariant local operators on 10 sites for the anisotropic six-vertex model on a cylinder with generic Matsubara data. This is equivalent to the generalised Gibbs ensemble for the XXX spin chain. In the case when the \({\mathfrak {sl}}_{2}\) and C symmetries are not broken this computation is equivalent to finding the entire density matrix up to 10 sites. As application, we compute the entanglement entropy without and with temperature, and compare the results with CFT predictions.


Integrable model XXX antiferromagnet Entanglement density matrix Entanglement entropy 



TM thanks to T. Ooura for suggesting his kernel function used in our calculation.


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Institute for Liberal Arts and SciencesKyoto UniversityKyotoJapan
  2. 2.UPMC Univ Paris 06, CNRS, UMR 7589, LPTHESorbonne UniversitéParisFrance

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