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>The <strong>spin</strong>-1/2 <strong>XXZ</strong> Heisenberg <strong>chain</strong>H = ∑ M(m=1 σxm σx m+1 + σy m σy m+1 + ∆ (σz m σz m+1 − 1)) − h ∑ M2 m=1 σz m• Hamiltonian eigenstates( A(λ)Algebraic Be<strong>the</strong> ansatz : σ α m −→ T (λ) = C(λ)B(λ)D(λ))T (λ) ≡ T a,1...N (λ) = L aN (λ − ξ N ) . . . L a1 (λ − ξ 1 )L an (λ) being 2 × 2 matrices with entries function <strong>of</strong> σ x,y,znoperators in site n.Yang-Baxter algebra : R 12 (λ 1 , λ 2 )T 1 (λ 1 )T 2 (λ 2 ) = T 2 (λ 2 )T 1 (λ 1 )R 12 (λ 1 , λ 2 )Commuting conserved charges : t(λ) = A(λ) + D(λ), [t(λ), t(µ)] = 0– Typeset by FoilTEX – Florence 2003 4