Correlation functions of the XXZ spin-1/2 chain: recent progress

J. M. Maillet Correlation functionsThus for large m, one can replace sums over the set {λ ′ } by integrals. Now estimate thebehavior of F ({λ ′ }, m) for large m using :det m(−i sin ζsinh(λ ′ j − ξ k) sinh(λ ′ j − ξ k − iζ)(−→ (−2πi) m det m δ jk − K(λ′ j − λ′ k ) ) (2πimρ(λ ′ k ) det m)i2ζ sinh π ζ (λ′ j − ξ k)),with Lieb kernelHence :K(λ) =−i sin 2ζsinh(λ − iζ) sinh(λ + iζ)τ(m) −→( πζ) m2e m2 S 0 +o(m 2) , m → ∞,– Typeset by FoilTEX – Florence 2003 15