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We present an algorithm for the calculation of eigenstates with definite linear momentum in quantum lattices. Our method is related to the density matrix renormalization group, and makes use of the distribution of multipartite entanglement to build variational wave functions with translational symmetry. The algorithm is applied to the study of bilinear-biquadratic $S=1$ chains, in particular to the region of phase space between the dimerized and ferromagnetic phases.
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Porras et al. (2006) studied this question.
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