标题： 从实空间重正化群的角度看二维与三维的本质区别 显示英文标题

标题： Essential difference between 2D and 3D from the perspective of real-space renormalization group

摘要： 我们指出，量子信息概念的面积定律表明了块变换作为良好行为的实空间重正化群（RG）映射的局限性，这反过来指导了更好RG方案的设计。 互信息的面积定律意味着由于块边界上自旋的短尺度相关性的增长，在二维（2D）或更高维度中，Kadanoff的块自旋方法面临困难。 从后来的观点看，转向张量网络RG是受互信息指导的，并且由于其混合了量子和经典视角以及二维中的纠缠熵饱和，因此在二维中是高效的。 然而在三维（3D）中，纠缠按照面积定律增长，这对3D块张量映射作为合适的RG变换构成了威胁。 作为数值证据，我们展示了保留更多耦合项对3D伊辛模型临界指数估计的改进失败。 作为继续前进的指导，提出一个张量网络玩具模型以捕捉三维纠缠熵的面积定律。 显示英文摘要

摘要： We point out that area laws of quantum-information concepts indicate limitations of block transformations as well-behaved real-space renormalization group (RG) maps, which in turn guides the design of better RG schemes. Mutual-information area laws imply the difficulty of Kadanoff's block-spin method in two dimensions (2D) or higher due to the growth of short-scale correlations among the spins on the boundary of a block. A leap to the tensor-network RG, in hindsight, follows the guidance of mutual information and is efficient in 2D, thanks to its mixture of quantum and classical perspectives and the saturation of entanglement entropy in 2D. In three dimensions (3D), however, entanglement grows according to the area law, posing a threat to 3D block-tensor map as an apt RG transformation. As a numerical evidence, we show that estimations of 3D Ising critical exponents fail to improve by retaining more couplings. As a guidance to proceed, a tensor-network toy model is proposed to capture the 3D entanglement-entropy area law.