论文标题
Grassmann张量重新归一化组的债券加权方法
Bond-weighting method for the Grassmann tensor renormalization group
论文作者
论文摘要
最近，已提出张量网络描述其边缘上具有粘结权重的，以作为张量重新归一化组算法的新型改进。键的权重由单个高参数控制，其最佳值在原始工作中通过二维临界ISING模型的数值计算估算。我们开发了这种键加权的张量重新归一化组算法，以使其适用于费米子系统，并通过二维无质量的Wilson Fermion进行基准测试。我们表明，固定键维的准确性在费米子系统中也得到了提高，并提供了数值证据，表明超参数的最佳选择不受系统是否是骨或费米金的影响。此外，通过监视奇异值频谱，我们发现重新归一化的Grassmann Tensor的规模不变结构通过键加权技术成功保存。
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.
