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

J. M. Maillet Correlation functionsIdea of the proof :τ(m) =×m∏a>b( i2ζ sin ζ) m ( πζ)m 2 −m2sinh π ζ (λ a − λ b )∫Dd m λ · F ({λ}, m)sinh(λ a − λ b − iζ) sinh(λ a − λ b + iζ)(m∏ sinh(λa − iζ 2 ) sinh(λ a + iζ 2 )) m,a=1cosh π ζ λ awithF ({λ}, m) =limξ 1 ,...ξm→− iζ 2m∏a>b()1−i sin ζdet msinh(λsinh(ξ a − ξ b )j − ξ k ) sinh(λ j − ξ k − iζ)Integration domain D ≡ −∞ < λ 1 < λ 2 < · · · < λ m < ∞. Then at the saddle pointdistribution of λ’s can be described by a density function ρ(λ ′ ):ρ(λ ′ j ) = limm→∞1m(λ ′ j+1 − λ′ j )– Typeset by FoilTEX – Florence 2003 14