# Hidden Grassmann Structure in the XXZ Model III: Introducing Matsubara direction

Abstract : We address the problem of computing temperature correlation functions of the XXZ chain, within the approach developed in our previous works. In this paper we calculate the expected values of a fermionic basis of quasi-local operators, in the infinite volume limit while keeping the Matsubara (or Trotter) direction finite. The result is expressed in terms of two basic quantities: a ratio $\rho(\z)$ of transfer matrix eigenvalues, and a nearest neighbour correlator $\omega(\z,\xi)$. We explain that the latter is interpreted as the canonical second kind differential in the theory of deformed Abelian integrals.
Document type :
Journal articles
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https://hal.archives-ouvertes.fr/hal-00346751
Contributor : Fedor Smirnov Connect in order to contact the contributor
Submitted on : Friday, December 12, 2008 - 11:47:55 AM
Last modification on : Thursday, December 10, 2020 - 11:07:42 AM

### Citation

M. Jimbo, T. Miwa, F. Smirnov. Hidden Grassmann Structure in the XXZ Model III: Introducing Matsubara direction. Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2009, A42 (30), pp.304018. ⟨10.1088/1751-8113/42/30/304018⟩. ⟨hal-00346751⟩

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