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

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J. M. Maillet Correlation functionsPhysical correlation functionsExample :〈ψ g |σ + 1 σ− m+1 |ψ g〉 ≡ 〈ψ g |E 121m∏j=2(E 11j+ E 22j) E21 m+1 |ψ g〉−→ sum of 2 m−1 elementary blocks: 〈ψ g |C( η 2 ) (A + D)m−1 ( η 2 ) B(η 2 )|ψ g〉Compact and symmetrized formula for the multiple action of A + D operators−→ Two point correlation functions :m−1〈σ α 1 σβ m+1 〉 = ∑n=0∮Cz∫ ∫d n+1 z d n λC λCµd 2 µ [f({λ, z})] m Γ αβn({λ, µ, z}) S h({λ, z})−→ Gives directly known free fermion results setting ∆ = 0−→ Asymptotics of two point functions for general ∆?– Typeset by FoilTEX – Florence 2003 9
J. M. Maillet Correlation functionsEmptiness formation probabilityfor ∆ = cos ζ, 0 < ζ < π :τ(m) =limξ 1 ,...ξm→− iζ 21m!τ(m) = 〈ψ g |∫ ∞−∞m∏k=11 − σ z k|ψ g 〉2()Z m ({λ}, {ξ})idet m∏m2ζ sinhsinh(ξ a − ξ b )π ζ (λ j − ξ k )abFor ζ = π/3 : τ(m) = ( )1 m2 ∏ m−12 k=0( √3 ) 3m2(3k+1)!(m+k)! → c 2m − 36, 5m → ∞– Typeset by FoilTEX – Florence 2003 10
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Correlation functions of the XXZ spin-1/2 chain: recent progress

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