Computation of dynamical correlation functions of the spin-1 Babujan-Takhtajan chain

Abstract: The dynamical structure factor of the Babujan-Takhtajan antiferromagnetic spin-1 chain is computed numerically at zero temperature and zero magnetic field, using the higher-spin generalization of an Algebraic Bethe Ansatz-based method previously used for spin-1/2 integrable chains. This method, which consists in the explicit construction of eigenstates and the summation of the Lehmann representation of the correlator, is here particularly challenging to implement in view of the presence of strongly deviated string solutions to the Bethe equations. We show that a careful treatment of these deviations makes it possible to obtain perfect saturation of sum rules for small system sizes, and extremely good saturation for large system sizes where the dynamical structure factor is computed by including all two-spinon and four-spinon contributions. The real-space spin-spin correlation, obtained by Fourier transforming our results, displays asymptotics fitting predictions from conformal field theory.