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We report our density matrix renormalization-group and analytical work on S=1antiferromagnetic Heisenberg spin chains. We study the finite size behaviorwithin the framework of the non-linear sigma model. We study the effect ofmagnon-magnon interactions on the finite size spectrum and on the magnetizationcurve close to the critical magnetic field, determine the magnon scatteringlength and compare it to the prediction from the non-linear $\sigma$ model.Comment: 28 pages, 8 figures, made substantial improvement

physical review. b, condensed matter

Finite-size spectrum, magnon interactions, and magnetization of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mn /></mml:math>Heisenberg spin chains

Finite-size spectrum, magnon interactions, and magnetization ofS=1Heisenberg spin chains