Matrix product states represent ground states faithfully

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  • 4 October 2005
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. We also investigate the convex set of local reduced density operators of translational invariant systems. 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. This implies that a quantum computer may gives us only restricted help when determining the properties of ground states in 1-D quantum spin systems.

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