Second Renormalization of Tensor-Network States

Tao Xiang, Hui‐Hai Zhao, Z. Y. Xie +2 more

Zheng‐Cheng Gu, Frank Verstraete, Xiao-Gang Wen

Tao Xiang, Hui‐Hai Zhao, Q. N. Chen +3 more

Z. Y. Xie, Hong‐Chen Jiang, Qiaoni Chen +2 more

We propose a second renormalization group method to handle the tensor-network states or models. This method dramatically reduces the truncation error of the tensor renormalization group. It allows physical quantities of classical tensor-network models or tensor-network ground states of quantum systems to be accurately and efficiently determined.

Hui‐Hai Zhao, Z. Y. Xie, Qiaoni Chen +3 more

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 tensor-network 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 tensor-network 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.

Wang Meng-Xiong, Cai Jian-Wei, Z. Y. Xie +3 more

We employ the second renormalization group method of tensor-network states to investigate thermodynamic properties of the ferromagnetic and antiferromagnetic Potts model on triangular lattices. From the temperature dependence of the internal energy and the specific heat, both the critical temperatures and critical exponents are evaluated. For the q = 3 antiferromagnetic Potts model, the critical temperature is found to be T c = 0.627163±0.000003, which is at least one order of magnitude more accurate than that obtained by other methods.