论文标题
经典统计模型的变分转移矩阵重新归一化组方法
Variational corner transfer matrix renormalization group method for classical statistical models
论文作者
论文摘要
在张量网络状态的情况下，我们首次将角传递矩阵重质化组（CTMRG）方法重新加密为变异的双层优化算法。优化问题的解决方案对应于常规CTMRG方法中提出的定点环境，从中可以有效地评估由无限张量网络表示的经典统计模型的分区函数。通过对二聚体模型的残留熵进行高精度计算，通过研究经典自旋模型中的几种典型相变，获得的临界点和关键指数都与文献中最著名的结果一致，可以进一步验证这种变异思想的有效性。它扩展到三维张量网络或量子晶格模型非常简单，也简要讨论。
In the context of tensor network states, we for the first time reformulate the corner transfer matrix renormalization group (CTMRG) method into a variational bilevel optimization algorithm. The solution of the optimization problem corresponds to the fixed-point environment pursued in the conventional CTMRG method, from which the partition function of a classical statistical model, represented by an infinite tensor network, can be efficiently evaluated. The validity of this variational idea is demonstrated by the high-precision calculation of the residual entropy of the dimer model, and is further verified by investigating several typical phase transitions in classical spin models, where the obtained critical points and critical exponents all agree with the best known results in literature. Its extension to three-dimensional tensor networks or quantum lattice models is straightforward, as also discussed briefly.
