标题： 投影纠缠对态在三角晶格上的变分优化 显示英文标题

标题： Variational optimization of projected entangled-pair states on the triangular lattice

摘要： 我们引入了一种通用的角转移矩阵重正化群算法，专门针对三角晶格上的投影纠缠对态。 通过集成自动微分，我们的方法能够在该晶格几何上直接进行变分能量最小化。 与传统方法将三角晶格映射到具有对角次近邻相互作用的正方形晶格不同，我们的原生公式在相同的键维下得到了改进的变分结果。 这种改进源于张量网络中更忠实且物理上合理的纠缠结构表示以及变分参数数量的增加。 我们将该方法应用于三角晶格和凯库勒晶格上的反铁磁最近邻海森堡模型，并将结果与之前的数值研究进行对比。 显示英文摘要

摘要： We introduce a general corner transfer matrix renormalization group algorithm tailored to projected entangled-pair states on the triangular lattice. By integrating automatic differentiation, our approach enables direct variational energy minimization on this lattice geometry. In contrast to conventional approaches that map the triangular lattice onto a square lattice with diagonal next-nearest-neighbour interactions, our native formulation yields improved variational results at the same bond dimension. This improvement stems from a more faithful and physically informed representation of the entanglement structure in the tensor network and an increased number of variational parameters. We apply our method to the antiferromagnetic nearest-neighbour Heisenberg model on the triangular and kagome lattice, and benchmark our results against previous numerical studies.