Bond-weighting method for the Grassmann tensor renormalization group

TL;DR

This paper extends the bond-weighted tensor renormalization group method to fermionic systems, demonstrating improved accuracy and preserving scale-invariance, with implications for analyzing complex quantum systems.

Contribution

The authors adapt the bond-weighted tensor renormalization group to fermionic systems and show it improves accuracy and maintains scale-invariance, regardless of bosonic or fermionic nature.

Findings

Improved accuracy in fermionic systems with fixed bond dimension.

Optimal hyperparameter choice is system-independent.

Scale-invariant structure of Grassmann tensor is preserved.

Abstract

Recently, the tensor network description with bond weights on its edges has been proposed as a novel improvement for the tensor renormalization group algorithm. The bond weight is controlled by a single hyperparameter, whose optimal value is estimated in the original work via the numerical computation of the two-dimensional critical Ising model. We develop this bond-weighted tensor renormalization group algorithm to make it applicable to the fermionic system, benchmarking with the two-dimensional massless Wilson fermion. We show that the accuracy with the fixed bond dimension is improved also in the fermionic system and provide numerical evidence that the optimal choice of the hyperparameter is not affected by whether the system is bosonic or fermionic. In addition, by monitoring the singular value spectrum, we find that the scale-invariant structure of the renormalized Grassmann tensor is successfully kept by the bond-weighting technique.