Hidden Grassmann structure in the XXZ model III: introducing the Matsubara direction

2008/11/29 by M. Jimbo, M Jimbo, T. Miwa +3 · 6 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #Quantum many-body systems #hep-th #math-ph #math.MP

paper · pdf · doi:10.1088/1751-8113/42/30/304018

published as J.Phys.A42:304018,2009 · 35p, 1 figure

arxiv created 2008/11/29 · openalex publication_date 2009/07/14 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

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

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