论文标题
Q状态时钟模型的准确模拟
Accurate simulation of q-state clock model
论文作者
论文摘要
我们通过使用最先进的环路循环优化对张量的网络renormalzation（LOOP-TNR）算法来准确模拟平方晶格上$ q $ state时钟模型的相图和关键行为。 $ Q \ geq 5 $的两个相转换点的精度非常高。此外，通过计算共形缩放尺寸，我们能够准确地确定两个相转换点的压缩玻色子理论的压实半径$ r $。特别是，高温关键点的紧凑型半径$ r $与Berezinskii-Kosterlitz-thouless（BKT）过渡的预测$ r $完全相同。此外，我们发现，对于足够大的$ Q $，高温临界点处的固定点张量也会收敛于同一次数，而相应的运算符产品扩展（OPE）系数也可以直接从固定点tensor中直接读取。
We accurately simulate the phase diagram and critical behavior of the $q$-state clock model on the square lattice by using the state-of-the-art loop optimization for tensor network renormalzation(loop-TNR) algorithm. The two phase transition points for $q \geq 5$ are determined with very high accuracy. Furthermore, by computing the conformal scaling dimensions, we are able to accurately determine the compactification radius $R$ of the compactified boson theories at both phase transition points. In particular, the compactification radius $R$ at high-temperature critical point is precisely the same as the predicted $R$ for Berezinskii-Kosterlitz-Thouless (BKT) transition. Moreover, we find that the fixed point tensors at high-temperature critical point also converge(up to numerical errors) to the same one for large enough $q$ and the corresponding operator product expansion(OPE) coefficient of the compactified boson theory can also be read out directly from the fixed point tensor.
