  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.
