论文标题
XY模型中对数校正指数的张量网络计算
Tensor network calculation of the logarithmic correction exponent in the XY model
论文作者
论文摘要
我们通过使用张量重构量化组方法研究了在正方晶格上经典$ XY $模型中第一个Lee-Yang（LY）零的对数校正的对数校正。在比较高阶张量重新归一致化组（HOTRG）和循环优化的张量网络重重程（LOOPTNR）时，我们发现LOOPTNR中的纠缠过滤对于获得较高的对数位置的近似键合的准确性至关重要，而Hotrg的表征仍然相差，而Hotrg的位置则与较高的键合中的键合，而键合的位置则是零的键合。奇异价值分解和倾斜投影仪。使用$ l \ times l $ lattices中$ l = 1024 $计算的LOOPTNR数据，我们估计来自有限大小的有效指数的外推的对数校正指数$ r = -0.0643（9）$，可与en Renormization Group the Renormization Group the Renormalization Group of $ renoralization Group the $ R = -1 $ R = -1 16/16。
We study the logarithmic correction to the scaling of the first Lee-Yang (LY) zero in the classical $XY$ model on square lattices by using tensor renormalization group methods. In comparing the higher-order tensor renormalization group (HOTRG) and the loop-optimized tensor network renormalization (LoopTNR), we find that the entanglement filtering in LoopTNR is crucial to gaining high accuracy for the characterization of the logarithmic correction, while HOTRG still proposes approximate bounds for the zero location associated with two different bond-merging algorithms of the higher-order singular value decomposition and the oblique projectors. Using the LoopTNR data computed up to the system size of $L=1024$ in the $L \times L$ lattices, we estimate the logarithmic correction exponent $r = -0.0643(9)$ from the extrapolation of the finite-size effective exponent, which is comparable to the renormalization group prediction of $r = -1/16$.
