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 $ρ(\z)$ of transfer matrix eigenvalues, and a nearest neighbour correlator $ω(\z,ξ)$. We explain that the latter is interpreted as the canonical second kind differential in the theory of deformed Abelian integrals.

35p, 1 figure

References in corpus (7)

• Correlation functions of the XXZ Heisenberg spin-1/2 chain in a magnetic field
• Integrable Structure of Conformal Field Theory III. The Yang-Baxter Relation
• Integral representations for correlation functions of the XXZ chain at finite temperature
• Hidden Grassmann structure in the XXZ model
• Factorization of the finite temperature correlation functions of the XXZ chain in a magnetic field
• Structure of Matrix Elements in Quantum Toda Chain
• Baxter equations and Deformation of Abelian Differentials

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