Matrix product states represent ground states faithfully

TL;DR

This paper analyzes the effectiveness of matrix product states in approximating ground states of 1-D quantum systems, providing theoretical insights into their high accuracy and applicability to critical systems.

Contribution

It offers a quantitative analysis of matrix product states' approximation quality and explores the convex set of local reduced density operators, supporting the use of renormalization group algorithms.

Findings

Matrix product states approximate ground states with high fidelity.

Theoretical justification for renormalization group algorithms' accuracy.

Validation of MPS effectiveness even in critical systems.

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 justifies their use even in the case of critical systems.