论文标题
树木张量网络的自动结构优化
Automatic structural optimization of tree tensor networks
论文作者
论文摘要
树张量网络（TTN）为量子多体系统的实际模拟提供了一个必不可少的理论框架，其中由等轴测张量的连通性定义的网络结构在提高其近似准确性方面起着至关重要的作用。在本文中，我们提出了一种TTN算法，该算法使我们能够通过局部重新连接以及抑制腿上的双分部分纠缠熵来自动优化网络结构。该算法可以无缝地实现到像密度 - 矩阵重质化组这样的常规TTN方法。我们将算法应用于具有相互作用的层次空间分布的不均匀抗磁性海森堡自旋链。然后，我们证明，嵌入在系统的地面中的纠缠结构可以有效地将其视为优化的TTN中的完美二进制树。还讨论了算法的可能改进和应用。
Tree tensor network (TTN) provides an essential theoretical framework for the practical simulation of quantum many-body systems, where the network structure defined by the connectivity of the isometry tensors plays a crucial role in improving its approximation accuracy. In this paper, we propose a TTN algorithm that enables us to automatically optimize the network structure by local reconnections of isometries to suppress the bipartite entanglement entropy on their legs. The algorithm can be seamlessly implemented to such a conventional TTN approach as density-matrix renormalization group. We apply the algorithm to the inhomogeneous antiferromagnetic Heisenberg spin chain having a hierarchical spatial distribution of the interactions. We then demonstrate that the entanglement structure embedded in the ground-state of the system can be efficiently visualized as a perfect binary tree in the optimized TTN. Possible improvements and applications of the algorithm are also discussed.
