Renormalization of tensor-network states

By Hui Zhao, Zhiyuan Xie, Q. N. Chen, Zhongxu Wei, Jianwang Cai, Tao Xiang. 2010

132 citations recorded by the source corpus.

We have discussed the tensor-network representation of classical statistical or interacting quantum lattice models, and given a comprehensive introduction to the numerical methods we recently proposed for studying the tensor-network states/models in two dimensions. A second renormalization scheme is introduced to take into account the environment contribution in the calculation of the partition function of classical tensornetwork models or the expectation values of quantum tensor-network states. It improves significantly the accuracy of the coarse-grained tensor renormalization-group method. In the study of the quantum tensornetwork states, we point out that the renormalization effect of the environment can be efficiently and accurately described by the bond vector. This, combined with the imaginary-time evolution of the wave function, provides an accurate projection method to determine the tensor-network wave function. It reduces significantly the truncation error and enables a tensor-network state with a large bond dimension, which is difficult to be accessed by other methods, to be accurately determined.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/9c0f84ae7b1e50161b3406c83056e4a531a05a53

Citations in the corpus

• Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 1 Low-Rank Tensor Decompositions (2016, unknown): “The above tensor transformation procedure is quite general, and is applied in Figure 29 (b) to transform a Honey-Comb lattice into a tensor chain (TC) [288], while Figure 30 illustrates the conversion of a tensor chain (TC) into TT/MPS with OBC.”