Spin-1 antiferromagnetic Heisenberg chains in an external staggered field

We present in this paper a nonlinear a-model analysis of a spin-1 antiferro magnetic Heisenberg chain in an external commensurate staggered magnetic fi eld. After rediscussing briefly and extending previous results for the stag gered magnetization curve, the core of the paper is a calculation at the tr ee level, of the Green functions of the model. We obtain precise results fo r the elementary excitation spectrum and in particular for the spin gaps in the transverse and longitudinal channels. It is shown that, while the spec tral weight in the transverse channel is exhausted by a single magnon pole, in the longitudinal one, besides a magnon pole a two-magnon continuum appe ars as well whose weight is a steadily increasing function of the applied f ield, while the weight of the magnon decreases correspondingly. The balance between the two is governed by a sum rule that is derived and discussed. A detailed comparison with the present experimental and numerical state of t he art as well as with previous analytical approaches is also made.