Automatic structural optimization of tree tensor networks
Automatic structural optimization of tree tensor networks
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DOI：
10.1103/physrevresearch.5.013031
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发表时间：
2022-09
影响因子：
4.2
通讯作者：
T. Hikihara;H. Ueda;K. Okunishi;Kenji Harada;T. Nishino
中科院分区：
文献类型：
--
作者：
T. Hikihara;H. Ueda;K. Okunishi;Kenji Harada;T. Nishino
树张量网络（TTN）为量子多体系统的实际模拟提供了重要的理论框架，其中由等距张量的连通性定义的网络结构在提高其逼近精度方面发挥着至关重要的作用。在本文中，我们提出了一种 TTN 算法，该算法使我们能够通过等距的局部重连接来自动优化网络结构，以抑制其腿上的二分纠缠熵。该算法可以无缝地实现到诸如密度矩阵重整化群等传统TTN方法。我们将该算法应用于具有相互作用的分层空间分布的非均匀反铁磁海森堡自旋链。然后，我们证明嵌入系统基态的纠缠结构可以有效地可视化为优化 TTN 中的完美二叉树。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.