Ground States in Relatively Bounded Quantum Perturbations of Classical Lattice Systems

We consider ground states in relatively bounded quantum perturbations of classical lattice models. We prove general results about such perturbations (existence of the spectral gap, exponential decay of truncated correlations, analyticity of the ground state), and also prove that in particular the AKLT model belongs to this class if viewed on a large enough length scale. This immediately implies a general perturbation theory about this model. On leave from Institute for Information Transmission Problems, Moscow The author is an Irish Research Council for Science, Engineering and Technology Postdoctoral Fellow