Loop Optimization for Tensor Network Renormalization

• Main Authors: Yang, Shuo (Author), Gu, Zheng-Cheng (Author), Wen, Xiao-Gang (Contributor)
• Other Authors: Massachusetts Institute of Technology. Department of Physics (Contributor)
• Format: Article
• Language: English
• Published: American Physical Society, 2017-03-16T20:43:14Z.
• Subjects: Article
• Online Access: Get fulltext

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.
National Natural Science Foundation (China) (11274192)
BMO Financial Group
Templeton Foundation
National Science Foundation (U.S.) (Grants DMR-1506475 and PHY11-25915)