Matrix product states approximate ground states faithfully

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Abstract
We quantify how well matrix product states approximate exact ground states of 1-D quantum spin systems as a function of the number of spins and the entropy of blocks of spins. The results give a theoretical justification for the high accuracy of renormalization group algorithms, and give strong indications that the computational complexity for simulating 1-D quantum systems is P. We also investigate the convex set of local reduced density operators of translational invariant systems.

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