论文标题
三维张量网络的有效计算
Efficient calculation of three-dimensional tensor networks
论文作者
论文摘要
我们已经提出了一种有效的算法来计算平移不变的三维张量网络中的物理量，该网络与三维经典统计模型的研究以及（2+1）维量子量子lattice模型特别相关。在经典模型的背景下，我们通过求解转移矩阵的主要特征值问题来确定分区功能，其左右主流特征向量由两个预测的纠缠单纯形态表示。这两个预计的纠缠单纯形状态不是彼此之间的Hermitian共轭，而是适当排列，因此可以比通常的处方更有效地计算其内部产品。对于三维ISING模型，计算出的内部能量和自发磁化与文献中已发布的结果相符。还讨论了可能的改进和扩展到其他模型。
We have proposed an efficient algorithm to calculate physical quantities in the translational invariant three-dimensional tensor networks, which is particularly relevant to the study of the three-dimensional classical statistical models and the (2+1)-dimensional quantum lattice models. In the context of a classical model, we determine the partition function by solving the dominant eigenvalue problem of the transfer matrix, whose left and right dominant eigenvectors are represented by two projected entangled simplex states. These two projected entangled simplex states are not Hermitian conjugate to each other but are appropriately arranged so that their inner product can be computed much more efficiently than in the usual prescription. For the three-dimensional Ising model, the calculated internal energy and spontaneous magnetization agree with the published results in the literature. The possible improvement and extension to other models are also discussed.
