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We introduce a general analytic approach to the study of factorization pointsand factorized ground states in quantum cooperative systems. The method allowsto determine rigorously existence, location, and exact form of separable groundstates in a large variety of, generally non-exactly solvable, spin modelsbelonging to different universality classes. The theory applies totranslationally invariant systems, irrespective of spatial dimensionality, andfor spin-spin interactions of arbitrary range.

Theory of ground state factorization in quantum cooperative systems