Triad second renormalization group

We propose a second renormalization group (SRG) in the triad representation of tensor networks. The SRG method improves two parts of the triad tensor renormalization group, which are the decomposition of intermediate tensors and the preparation of isometrics, taking the influence of environment tensors into account. Every fundamental tensor including environment tensor is given as a rank-3 tensor, and the computational cost of the proposed algorithm scales with O(chi(5)) employing the randomized SVD where chi is the bond dimension of tensors. We test this method in the classical Ising model on the two dimensional square lattice, and find that numerical results are obtained in good accuracy for a fixed computational time.

Automated summary

In this research, we propose a second renormalization group (SRG) method based on the triad representation of tensor networks. The SRG method improves the decomposition and isometric preparation of the triad tensor, taking into account the influence of environment tensors. Numerical results obtained in the classical Ising model on the two-dimensional square lattice show good accuracy with a fixed computational time.