Murg V, Verstraete F, Schneider R, Nagy P R, Legeza Ö
J Chem Theory Comput. 2015 Mar 10;11(3):1027-36. doi: 10.1021/ct501187j.
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.
我们研究了用于量子化学的具有可变张量阶数的树张量网络态（TTNS）方法。TTNS是一种变分方法，用于以张量积形式有效近似完全活性空间（CAS）组态相互作用（CI）波函数。TTNS可被视为矩阵乘积态（MPS）方法的高阶推广。MPS波函数被表述为在跨越原始CAS-CI问题的截断希尔伯特空间的多粒子基中矩阵的乘积。这些矩阵属于按一维阵列组织的活性轨道，而TTNS中的张量是根据相同轨道的树状排列定义的。树结构具有优势，因为树中任意两个轨道之间的距离仅与轨道数N呈对数比例缩放，而在MPS阵列中缩放是线性的。从计算成本的角度来看，在两种排列中将强相关轨道保持在附近是有益的；因此，TTNS假设更适合具有大量高度相关轨道的多参考问题。为了利用TTNS的优势，设计了一种基于量子信息理论和纠缠来优化树张量网络拓扑的新算法。在LiF的离子 - 中性避免交叉中展示了TTNS方法的卓越性能。还表明，仅使用基态性质，即单轨道纠缠，就可以定位LiF的避免交叉。
