Spectral Functions of the Bilinear-Biquadratic Spin-1 Chain

The bilinear-biquadratic spin-1 chain exhibits a rich phase diagram. Depending on the two coupling strengths, the system can be in a ferromagnetic phase, a gapped dimer phase, the gapped Haldane phase with hidden topological long-range order, or an extended critical phase with period-three structure and dominant quadrupolar correlations. Here, we use density matrix renormalization group (DMRG) algorithms to compute precise static structure factors and spectral functions in the different phases. We relate our results to insights from exact solutions at special points in the phase diagram and field-theoretical approaches.