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

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We calculate the excitation spectrum and spectral weights of the alternating antiferromagnetic-ferromagnetic spin-half Heisenberg chain with exchange couplings J and -|λ|J as a power series in λ. For small |λ|, 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 |λ| 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 |λ| confirms that the ground state energy and excitation gap map onto those of the spin-one chain.