arXiv:1512.04938 · Physical Review Letters

Loop Optimization for Tensor Network Renormalization

Shuo Yang, Zheng‐Cheng Gu, Xiao-Gang Wen

Published Mar 15, 2017• 167 citations

Abstract

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.

DOI: 10.1103/physrevlett.118.110504

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