Approximating local properties by tensor network states with constant bond dimension

2019/03/24 by Huang, Yichen
#FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Strongly Correlated Electrons (cond-mat.str-el)

paper · doi:10.48550/arxiv.1903.10048

Abstract

Suppose we would like to approximate all local properties of a quantum many-body state to accuracy δ. In one dimension, we prove that an area law for the Renyi entanglement entropy R_α with index α<1 implies a matrix product state representation with bond dimension poly(1/δ). For (at most constant-fold degenerate) ground states of one-dimensional gapped Hamiltonians, it suffices that the bond dimension is almost linear in 1/δ. In two dimensions, an area law for R_α(α<1) implies a projected entangled pair state representation with bond dimension e^O(1/δ). In the presence of logarithmic corrections to the area law, similar results are obtained in both one and two dimensions.

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