Crossover of spectral features from Dimerized to Haldane behavior in alternating antiferromagnetic-ferromagnetic spin-half chains

We calculate the excitation spectrum and spectral weights of the alternating antiferromagnetic-ferromagnetic spin-half Heisenberg chain with exchange couplings $J$ and $-|\lambda|J$ as a power series in $\lambda$. For small $|\lambda|$, the gapped one-particle spectrum has a maximum at $k=0$ and there is a rich structure of bound (and anti-bound) states below (and above) the 2-particle continuum. As $|\lambda|$ is increased past unity the spectrum crosses over to the Haldane regime, where the peak shifts away from $k=0$, the one particle states merge with the bottom of the continuum near $k=0$, and the spectral weights associated with the one-particle states become very small. Extrapolation of the spectrum to large $|\lambda|$ confirms that the ground state energy and excitation gap map onto those of the spin-one chain.