We show a way to perform the canonical renormalization group (RG) prescription in tensor space: write down the tensor RG equation, linearize it around a fixed-point tensor, and diagonalize the resulting linearized RG equation to obtain scaling dimensions. The tensor RG methods have had great success in producing accurate free energy compared with the conventional real-space RG schemes. However, the above-mentioned canonical procedure has not been implemented for general tensor-network-based RG schemes. We extend the success of the tensor methods further to extraction of scaling dimensions through the canonical RG prescription, without explicitly using the conformal field theory. This approach is benchmarked in the context of the Ising models in one dimension and two dimensions. Based on a pure RG argument, the proposed method has potential applications to three-dimensional systems, where the existing bread-and-butter method is inapplicable.

中文翻译：

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线性化张量重归一化组变换的尺度尺寸

我们展示了一种在张量空间中执行规范化重整化组（RG）处方的方法：写下张量RG方程，将其线性化在定点张量附近，对角化所得的线性化RG方程以获得缩放尺寸。与传统的实空间RG方案相比，张量RG方法在产生准确的自由能方面取得了巨大的成功。但是，上述常规过程尚未针对基于常规张量网络的RG方案实施。我们将张量方法的成功扩展到通过典范的RG处方提取比例尺，而无需明确使用保形场理论。在一维和二维伊辛模型的上下文中对该方法进行了基准测试。基于纯RG的论点，