Spin–spin correlation functions of the XXZ-12 Heisenberg chain in a magnetic field Original Research Article

Using algebraic Bethe ansatz and the solution of the quantum inverse scattering problem, we compute compact representations of the spin–spin correlation functions of the XXZ-12 Heisenberg chain in a magnetic field. At lattice distance m, they are typically given as the sum of m terms. Each term n of this sum, n=1,…,m, is represented in the thermodynamic limit as a multiple integral of order 2n+1; the integrand depends on the distance as the power m of some simple function. The root of these results is the derivation of a compact formula for the multiple action on a general quantum state of the chain of transfer matrix operators for arbitrary values of their spectral parameters.