Document Type


Date of Original Version



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 cosθ) and biquadratic (J sinθ) exchange are investigated via the recursion method for systems with up to N sites over the predicted range, −π/4 < θ ≲ π/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 θ = arctan 1/3 (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 (ST = 1), by continua of two-magnon scattering states (ST = 0, 1, 2), and by discrete branches of two-magnon bound states with positive interaction energy ( The dimer and trimer spectra at q = π are found to consist of single modes with N-independent excitation energies ωDλ/|e0| = 5 and ωTλ/|e0| = 6, where e0=E0/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 (θ = −π/4), the two-magnon excitations turn into two-spinon excitations.

Publisher Statement

© 1998 The American Physical Society