Master equation for spin–spin correlation functions of the XXZ chain

2004/06/22 by N. Kitanine, N Kitanine, J. M. Maillet +3 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Quantum many-body systems #hep-th

paper · pdf · doi:10.1016/j.nuclphysb.2005.01.050

published as Nucl.Phys. B712 (2005) 600-622 · 24 pages

arxiv created 2004/06/22 · openalex publication_date 2005/02/25 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We derive a new representation for spin-spin correlation functions of the finite XXZ spin-1/2 Heisenberg chain in terms of a single multiple integral, that we call the master equation. Evaluation of this master equation gives rise on the one hand to the previously obtained multiple integral formulas for the spin-spin correlation functions and on the other hand to their expansion in terms of the form factors of the local spin operators. Hence, it provides a direct analytic link between these two representations of the correlation functions and a complete re-summation of the corresponding series. The master equation method also allows one to obtain multiple integral representations for dynamical correlation functions.

Citations

• Quantum Inverse Scattering Method and Correlation Functions
• Spin-spin correlation functions for the two-dimensional Ising model: Exact theory in the scaling region
• Infinite conformal symmetry in two-dimensional quantum field theory
• THE QUANTUM METHOD OF THE INVERSE PROBLEM AND THE HEISENBERG XYZ MODEL
• Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition
• Two soluble models of an antiferromagnetic chain

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