We study the spectral function $S(k,\omega )$ for the spin-1, one dimensional antiferromagnetic chain using a time-dependent density matrix renormalizaton group numerical method. We develop methods for extrapolating the time-dependent correlation functions to larger times in order to enhance the frequency resolution. The resulting spectral functions are impressively precise and accurate. Our results confirm many qualitative expectations from nonlinear $\sigma$ model methods and test them quantitatively. The critical wave vector at which the single particle excitation emerges from the two-particle continuum is estimated to be $0.23\pi –0.24\pi$.

• Received 7 January 2008

DOI:https://doi.org/10.1103/PhysRevB.77.134437