Low-energy physics of the bilinear-biquadratic spin-1 chain

The bilinear-biquadratic spin-1 chain features various interesting quantum phases, including the Haldane phase, a dimerized phase, and an extended critical phase. Here, we apply an efficient density matrix renormalization group (DMRG) algorithm utilizing infinite boundary conditions to compute precise dynamic spin structure factors for a comprehensive set of points in the phase diagram. Analyzing both dynamic spin and quadrupolar correlations, we gain detailed insights into the nature of low-lying excitations of the model. We compare our results to Bethe ansatz solutions at the SU(3)-symmetric ULS point and the TB point as well as at the pure biquadratic point, which can be mapped to an anisotropic spin-1/2 XXZ chain in the gapped Néel phase. In the Haldane phase, we relate our results to the approximate description in terms of the non-linear sigma model.