Correlation functions of the XXZ spin-1/2 chain: recent progress
Correlation functions of the XXZ spin-1/2 chain: recent progress
Correlation functions of the XXZ spin-1/2 chain: recent progress
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J. M. Maillet <strong>Correlation</strong> <strong>functions</strong>For arbitrary ζ :limm→∞log τ(m)m 2 = log π ζ + 1 2where cosh η = cos ζ = ∆, 0 < ζ < π.∫R−i0dωωsinh ω ωζ2(π − ζ) cosh22,sinh πω ωζ2sinh2cosh ωζlimm→∞limm→∞For <strong>the</strong> XXX <strong>chain</strong> (∆ = 1, ζ = 0):log τ(m)= − 1 log 2, ∆ = 0,m 2 2log τ(m)= 3 m 2 2 log 3 − 3 log 2, ∆ = 1 2 ,limm→∞log τ(m)m 2= log(Γ(34 )Γ(1 2 ))Γ( 1 4 )≈ log(0.5991),– Typeset by FoilTEX – Florence 2003 13