从不动点张量和缺陷粗粒化中提取CFT数据的张量网络方法
Tensor Network Methods for Extracting CFT Data from Fixed-Point Tensors and Defect Coarse Graining
AI总结：
本研究利用张量网络方法从二维Ising模型临界点的不动点张量提取CFT数据，提出GILT+HOTRG方案处理点状缺陷，实现精确的两点和四点函数计算。
摘要：
我们提出了一项关于利用张量网络方法提取CFT数据的综合研究，特别是从二维经典Ising模型在临界温度附近的线性化张量重正化群（lTRG）的不动点张量中提取。通过两种不同的方法，我们通过引入格点上的缺陷并利用不动点张量，提取了算子标度维度和算子乘积展开（OPE）系数。我们还探讨了格点上的点状缺陷对粗粒化过程的影响。我们发现，粗粒化后的缺陷张量与从lTRG不动点方程获得的共形态之间存在对应关系。我们还分析了我们提出的针对具有点状缺陷的张量网络的粗粒化方案的能力和局限性，该方案包括图无关局部截断（GILT）和高阶张量重正化群（HOTRG）。我们的结果提供了对张量重正化群方案在粗粒化缺陷张量方面的能力和局限性的更好理解，并且我们表明，在特定条件下，GILT+HOTRG可用于给出精确的两点和四点函数。我们还发现，采用最小规范形式进一步提高了RG流的稳定性。
英文摘要：
We present a comprehensive study on the extraction of CFT data using tensor network methods, specially, from the fixed-point tensor of the linearized tensor renormalization group (lTRG) for the 2D classical Ising model near the critical temperature. Utilizing two different methods, we extract operator scaling dimensions and operator-product-expansion (OPE) coefficients by introducing defects on the lattice and by employing the fixed-point tensor. We also explore the effects of point-like defects in the lattice on the coarse-graining process. We find that there is a correspondence between coarse-grained defect tensors and conformal states obtained from lTRG fixed-point equation. We also analyze the capabilities and limitations of our proposed coarse-graining scheme for tensor networks with point-like defects, which includes graph independent local truncation (GILT) and higher-order tensor renormalization group (HOTRG). Our results provide a better understanding of the capacity and limitations of the tenor renormalization group scheme in coarse-graining defect tensors, and we show that GILT+HOTRG can be used to give accurate two- and four-point functions under specific conditions. We also find that employing the minimal canonical form further improves the stability of the RG flow.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
