Renormalization of tensor-network states

TL;DR

This paper introduces advanced renormalization techniques for tensor-network states, significantly improving the accuracy and efficiency of studying classical and quantum lattice models in two dimensions.

Contribution

It presents a second renormalization scheme that accounts for environment effects, enhancing the tensor renormalization group method's precision and enabling accurate large-bond-dimension tensor-network state calculations.

Findings

Improved accuracy of tensor network coarse graining.

Efficient environment effect representation with bond vectors.

Reduced truncation errors in tensor-network state determination.

Abstract

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 wavefunction, provides an accurate projection method to determine the tensor-network wavfunction. It reduces significantly the truncation error and enable a tensor-network state with a large bond dimension, which is difficult to be accessed by other methods, to be accurately determined.