Static and dynamic structure factors in the Haldane phase of the bilinear-biquadratic spin-1 chain

The excitation spectra of the T = 0 dynamic structure factors for the spin, dimer, and trimer fluctuation operators as well as for the center fluctuation operator in the one-dimensional S = 1 Heisenberg model with isotropic bilinear (J cos theta) and biquadratic (J sin theta) exchange are investigated via the recursion method for systems with up to N = 18 sites over the predicted range, - pi/4 < theta less than or similar to pi/4, of the topologically ordered Haldane phase. The four static and dynamic structure factors probe the ordering tendencies in the various coupling regimes and the elementary and composite excitations which dominate the T = 0 dynamics. At theta = arctan1/3 (valence-bond solid point), the dynamically relevant spectra in the invariant subspaces with total spin ST = 0,1,2 are dominated by a branch of magnon states (S-T = 1), by continua of two-magnon scattering states (S-T = 0,1,2), and by discrete branches of two-magnon bound states with positive interaction energy (ST = 0,2). The dimer and trimer spectra at q = pi are found to consist of single modes with N-independent excitation energies omega(lambda)(D)//e(0)/ = 5 and omega(lambda)(T)//e(0)/ = 6, where e(0) = E-0/N is the ground-state energy per site. The basic structure of the dynamically relevant excitation spectrum remains the same over a substantial parameter range within the Haldane phase. At the transition to the dimerized phase (theta = - pi/4), the two-magnon excitations turn into two-spinon excitations.