Entanglement bipartitioning and tree tensor networks
Entanglement bipartitioning and tree tensor networks
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DOI：
10.1093/ptep/ptad018
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发表时间：
2022-10
影响因子：
3.5
通讯作者：
K. Okunishi;H. Ueda;T. Nishino
中科院分区：
文献类型：
--
作者：
K. Okunishi;H. Ueda;T. Nishino
提出了一种利用纠缠二分割方法设计量子多体系统树张量网络（TTN）的优化网络结构的方法。给定一个精确的基态波函数，我们执行自旋团簇节点的顺序二分，以最小化互信息或最大损失的纠缠熵与分支被二分。我们表明，纠缠bipartitioning的16个网站产生的非平凡树网络结构的$S=1/2$海森堡模型在一个和两个维度。由此产生的TTN，使我们能够获得更好的变分能量，与标准的TTN，如均匀矩阵产品状态和完美的二叉树张量网络。
We propose the entanglement bipartitioning approach to design an optimal network structure of the tree-tensor-network (TTN) for quantum many-body systems. Given an exact ground-state wavefunction, we perform sequential bipartitioning of spin-cluster nodes so as to minimize the mutual information or the maximum loss of the entanglement entropy associated with the branch to be bipartitioned. We demonstrate that entanglement bipartitioning of up to 16 sites gives rise to nontrivial tree network structures for $S=1/2$ Heisenberg models in one and two dimensions. The resulting TTNs enable us to obtain better variational energies, compared with standard TTNs such as uniform matrix product state and perfect-binary-tree tensor network.