Optimized contraction scheme for tensor-network states
Abstract
In the tensor-network framework, the expectation values of two-dimensional quantum states are evaluated by contracting a double-layer tensor network constructed from initial and final tensor-network states. The computational cost of carrying out this contraction is generally very high, which limits the largest bond dimension of tensor-network states that can be accurately studied to a relatively small value. We propose an optimized contraction scheme to solve this problem by mapping the double-layer tensor network onto an intersected single-layer tensor network. This reduces greatly the bond dimensions of local tensors to be contracted and improves dramatically the efficiency and accuracy of the evaluation of expectation values of tensor-network states. It almost doubles the largest bond dimension of tensor-network states whose physical properties can be efficiently and reliably calculated, and it extends significantly the application scope of tensor-network methods.
Cite
@article{arxiv.1705.08577,
title = {Optimized contraction scheme for tensor-network states},
author = {Z. Y. Xie and H. J. Liao and R. Z. Huang and H. D. Xie and J. Chen and Z. Y. Liu and T. Xiang},
journal= {arXiv preprint arXiv:1705.08577},
year = {2017}
}
Comments
7 pages, 6 figures, accepted version for Phys. Rev. B. The title is changed for easier understanding