Reduction formula of form factors for the integrable spin-s XXZ chains and application to the correlation functions

Abstract

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 operators. Here they are given by the operator-valued matrix elements of the monodromy matrix of the spin-1/2 XXZ spin chain. In the paper we call an arbitrary matrix element of a local operator between two Bethe eigenstates a form factor of the operator. We derive all important formulas of the fusion method in detail. 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.

41 pages, no figures

References in corpus (6)

• Form factors of integrable Heisenberg (higher) spin chains
• An algebraic derivation of the eigenspaces associated with an Ising-like spectrum of the superintegrable chiral Potts model
• Correlation functions of the integrable higher-spin XXX and XXZ spin chains through the fusion method
• Correlation functions of the integrable isotropic spin-1 chain at finite temperature
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Cited by in corpus (3)

• Algebraic Bethe Ansatz approach to form factors and correlation functions of the cyclic eight-vertex solid-on-solid model
• Antiperiodic XXZ chains with arbitrary spins: Complete eigenstate construction by functional equations in separation of variables
• Quantum Group U_q(sl(2)) Symmetry and Explicit Evaluation of the One-Point Functions of the Integrable Spin-1 XXZ Chain