Reduction formula of form factors for the integrable spin-s XXZ chains and application to correlation functions. (English) Zbl 1456.82242
Summary: For the integrable spin-s XXZ chain we express explicitly any given spin-s form factor in terms of a sum over the scalar products of the spin-1/2 fundamental operators of the algebraic Bethe ansatz. Here, they are given by the operator-valued matrix elements of the monodromy matrix of the spin-1/2 XXZ spin chain. We derive the reduction formula of higher-spin form factors by the fusion method in detail. We call an arbitrary matrix element of a local operator between two Bethe eigenstates a form factor of the operator in this paper. We thus revise the derivation of the higher-spin XXZ form factors given in a previous paper. The revised method has several interesting applications in mathematical physics. For instance, we express the spin-s XXZ correlation function of an arbitrary entry at zero temperature in terms of a sum of multiple integrals.
MSC:
| 82B23 | Exactly solvable models; Bethe ansatz |
| 81R12 | Groups and algebras in quantum theory and relations with integrable systems |
| 81R50 | Quantum groups and related algebraic methods applied to problems in quantum theory |
| 82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
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