Tree Tensor Network State with Variable Tensor Order: An Efficient Multireference Method for Strongly Correlated Systems.
Tree Tensor Network State with Variable Tensor Order: An Efficient Multireference Method for Strongly Correlated Systems.
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DOI：
10.1021/ct501187j
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发表时间：
2015-03-10
影响因子：
5.5
通讯作者：
Legeza, Oe
中科院分区：
文献类型：
--
作者：
Murg, V.;Verstraete, F.;Schneider, R.;Nagy, P. R.;Legeza, Oe
研究了量子化学中的变张量阶数树张量网络态方法。TTNS是一种变分方法，可以有效地近似张量积形式的完全活性空间（CAS）组态相互作用（CI）波函数。TTNS可以被认为是矩阵乘积状态（MPS）方法的高阶推广。MPS波函数被制定为矩阵的产品在一个多粒子基础上跨越截断希尔伯特空间的原始CAS-CI问题。这些矩阵属于以一维阵列组织的活动轨道，而TTNS中的张量是在相同轨道的树状排列上定义的。树结构是有利的，因为树中的两个任意轨道之间的距离仅与轨道的数量N成几何比例，而在MPS阵列中比例是线性的。从计算成本的角度来看，在这两种安排中保持强相关轨道的紧密邻近是有益的;因此，TTNS方法更适合于具有许多高度相关轨道的多参考问题。为了充分利用TTNS的优点，基于量子信息理论和纠缠理论，设计了一种新的树型张量网络拓扑优化算法。TTNS方法的上级性能被说明在离子中性避免LiF交叉。它还表明，避免交叉的LiF可以本地化仅使用基态的属性，即单轨道纠缠。
We study the tree-tensor-network-state (TTNS) method with variable tensor orders for quantum chemistry. TTNS is a variational method to efficiently approximate complete active space (CAS) configuration interaction (CI) wave functions in a tensor product form. TTNS can be considered as a higher order generalization of the matrix product state (MPS) method. The MPS wave function is formulated as products of matrices in a multiparticle basis spanning a truncated Hilbert space of the original CAS-CI problem. These matrices belong to active orbitals organized in a one-dimensional array, while tensors in TTNS are defined upon a tree-like arrangement of the same orbitals. The tree-structure is advantageous since the distance between two arbitrary orbitals in the tree scales only logarithmically with the number of orbitals N, whereas the scaling is linear in the MPS array. It is found to be beneficial from the computational costs point of view to keep strongly correlated orbitals in close vicinity in both arrangements; therefore, the TTNS ansatz is better suited for multireference problems with numerous highly correlated orbitals. To exploit the advantages of TTNS a novel algorithm is designed to optimize the tree tensor network topology based on quantum information theory and entanglement. The superior performance of the TTNS method is illustrated on the ionic-neutral avoided crossing of LiF. It is also shown that the avoided crossing of LiF can be localized using only ground state properties, namely one-orbital entanglement.
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影响因子：
3.7
作者：
Legeza, Oers;Gebhard, Florian;Rissler, Joerg
通讯作者：
Rissler, Joerg
影响因子：
3.3
作者：
Marti, Konrad H.;Bauer, Bela;Verstraete, Frank
通讯作者：
Verstraete, Frank
影响因子：
4.4
作者：
BAUSCHLICHER, CW;LANGHOFF, SR
通讯作者：
LANGHOFF, SR
影响因子：
1.6
作者：
BERKMAN, O;VISHKIN, U
通讯作者：
VISHKIN, U
影响因子：
8.6
作者：
Legeza, O.;Solyom, J.;Noack, R. M.
通讯作者：
Noack, R. M.