Massless phases of Haldane-gap antiferromagnets in a magnetic field

The behavior of Haldane-gap antiferromagnets in a strong magnetic held is n ot universal. While the low-energy physics of the conventional one-dimensio nal spin-1 Heisenberg model in its magnetized regime is described by one in commensurate soft mode, other systems with somewhat perturbed coupling cons tants can possess two characteristic soft modes in a certain range of the f ield strength. Such a two-component Luttinger liquid phase is realized abov e the massive Haldane-gap phase, and in general above any massive nonmagnet ic phase, when the ground state exhibits short-range incommensurate fluctua tions already in the absence of the held.