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arXiv:1510.03333 · Physical review. B./Physical review. B

Tensor network algorithm by coarse-graining tensor renormalization on finite periodic lattices

Hui‐Hai Zhao, Z. Y. Xie, Tao Xiang, Masatoshi Imada

Published Mar 9, 2016• 40 citations
arXivHTMLPDF

Abstract

We develop coarse-graining tensor renormalization group algorithms to compute physical properties of two-dimensional lattice models on finite periodic lattices. Two different coarse-graining strategies, one based on the tensor renormalization group and the other based on the higher-order tensor renormalization group, are introduced. In order to optimize the tensor network model globally, a sweeping scheme is proposed to account for the renormalization effect from the environment tensors under the framework of second renormalization group. We demonstrate the algorithms by the classical Ising model on the square lattice and the Kitaev model on the honeycomb lattice, and show that the finite-size algorithms achieve substantially more accurate results than the corresponding infinite-size ones.

DOI
10.1103/physrevb.93.125115

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We introduce a tensor renormalization group scheme for coarse graining a two-dimensional tensor network that can be successfully applied to both classical and quantum systems on and off criticality. The key innovation in our scheme is to deform a 2D tensor network into small loops and then optimize the tensors on each loop. In this way, we remove short-range entanglement at each iteration step and significantly improve the accuracy and stability of the renormalization flow. We demonstrate our algorithm in the classical Ising model and a frustrated 2D quantum model.
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