Bond-weighted Tensor Renormalization Group

TL;DR

The paper introduces the bond-weighted tensor renormalization group (BTRG), an improved algorithm that enhances accuracy and preserves scale-invariance in tensor network computations, especially for critical systems, with minimal additional computational cost.

Contribution

BTRG generalizes the conventional TRG by adding bond weights, achieving better performance and fixed-point tensors, and maintaining scale-invariance at criticality.

Findings

BTRG outperforms conventional TRG and HOTRG at the same bond dimension.

BTRG maintains the singular value spectrum invariance at the critical point.

BTRG achieves high-accuracy tensor contractions with similar computational cost.

Abstract

We propose an improved tensor renormalization group (TRG) algorithm, the bond-weighted TRG (BTRG). In BTRG, we generalize the conventional TRG by introducing bond weights on the edges of the tensor network. We show that BTRG outperforms the conventional TRG and the higher-order tensor renormalization group with the same bond dimension, while its computation time is almost the same as that of TRG. Furthermore, BTRG can have non-trivial fixed-point tensors at an optimal hyperparameter. We demonstrate that the singular value spectrum obtained by BTRG is invariant under the renormalization procedure in the case of the two-dimensional Ising model at the critical point. This property indicates that BTRG performs the tensor contraction with high accuracy while keeping the scale-invariant structure of tensors.