Correlation length of the biquadratic spin-1 chain

We calculate the ground-state energy and correlation length of the spin-1 antiferromagnetic biquadratic chain, as well as the excitation energy of the two lowest-lying states. We use the equivalence of this model to the spin-1/2 XXZ chain for a specific anisotropy parameter. The XXZ model is solvable by the Bethe ansatz. We solve the Bethe ansatz equations numerically and obtain the correlation length from the ground-state energy of finite chains by use of a finite-size scaling ansatz. We find a surprisingly large correlation length. We also perform quantum Monte Carlo simulations which show clearly that the biquadratic chain dimerizes.