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

Abstract

The excitation spectra of the T=0 dynamic structure factors for the spin, dimer, and trimer fluctuation operators as well as for the newly defined center fluctuation operator in the one-dimensional S=1 Heisenberg model wi th isotropic bilinear $(J\cos \theta )$ and biquadratic $(J\sin \theta )$ exchange are investigated via the recursion method for systems with up to N=18 site s over the predicted range, $-\pi /4<\theta \lesssim \pi /4$, of the topologically ordered Haldane phase. The four static and dynamic structure factors probe t he ordering tendencies in the various coupling regimes and the elementary and composite excitations which dominate the T=0 dynamics. At $\theta =\arctan 1/3$ (VBS point), the dynamically relevant spectra in the invariant subspaces with total spin $S_T=0,1,2$ 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 $(S_T=0,2)$. The dimer and trimer spectra at $q=\pi$ ar e 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.

12 pages, 4 Postscript figures