Correlation functions of the integrable higher-spin XXX and XXZ spin chains through the fusion method. (English) Zbl 1204.82008
Summary: For the integrable higher-spin XXX and XXZ spin chains we present multiple-integral representations for the correlation function of an arbitrary product of Hermitian elementary matrices in the massless ground state. We give a formula expressing it by a single term of multiple integrals. In particular, we explicitly derive the emptiness formation probability (EFP). We assume \(2s\)-strings for the ground-state solution of the Bethe-ansatz equations for the spin-\(s\) XXZ chain, and solve the integral equations for the spin-\(s\) Gaudin matrix. In terms of the XXZ coupling \(\Delta \) we define \(\zeta \) by \(\Delta = \cos \zeta\), and put it in a region \(0\leq \zeta < \pi /2s\) of the gapless regime: \(-1<\Delta \leq 1\) \((0\leq \zeta < \pi )\), where \(\Delta =1\) \( (\zeta =0)\) corresponds to the antiferromagnetic point. We calculate the zero-temperature correlation functions by the algebraic Bethe-ansatz, introducing the Hermitian elementary matrices in the massless regime, and taking advantage of the fusion construction of the \(R\)-matrix of the higher-spin representations of the affine quantum group.
MSC:
| 82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
| 82B23 | Exactly solvable models; Bethe ansatz |
| 81R50 | Quantum groups and related algebraic methods applied to problems in quantum theory |
| 17B37 | Quantum groups (quantized enveloping algebras) and related deformations |
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