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

J. M. Maillet Correlation functionsτ(m, {ε j }) = (−1) m2 −m2 3 m 2 −m2 m ∏⎛⎜× det m ⎝∫ ∞−∞−mτ(m, {ε j }) = (−1)m2 2 ∏ m2 m2a>bsinh 3(ε b − ε a )sinh(ε b − ε a )m∏a,b=1a≠b1sinh(ε a − ε b )⎞dλ⎟4π cosh(λ − ε j ) sinh(λ − ε k − iπ 6 ) sinh(λ − ε k + iπ 6 ) ⎠a>bsinh 3(ε b − ε a )sinh(ε b − ε a )m∏a,b=1a≠bTake the homogeneous limit ε j → 0 (ξ k = ε k − iπ/6) :τ(m) = (−1) m2 −m2 3 m2 +m2 2−m2m−1⎛1sinh(ε a − ε )·det mb[ ]∏∂(n!) −2 j+k−2sinh x 2det m∂x j+k−2 sinh 3x 2n=0Can be computed using Kuperberg determinant identity⎝ 3 sinh ε j −ε k2sinh 3(ε j −ε k )2x=0⎞⎠– Typeset by FoilTEX – Florence 2003 12