T3NS: Three-Legged Tree Tensor Network States,Journal of Chemical Theory and Computation

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T3NS: Three-Legged Tree Tensor Network States
Journal of Chemical Theory and Computation ( IF 5.7 ) Pub Date : 2018-02-26 00:00:00 , DOI: 10.1021/acs.jctc.8b00098
Klaas Gunst _{1,

2} , Frank Verstraete _{2,

3} , Sebastian Wouters ₄ , Örs Legeza ₅ , Dimitri Van Neck ₁

Affiliation

We present a new variational tree tensor network state (TTNS) ansatz, the three-legged tree tensor network state (T3NS). Physical tensors are interspersed with branching tensors. Physical tensors have one physical index and at most two virtual indices, as in the matrix product state (MPS) ansatz of the density matrix renormalization group (DMRG). Branching tensors have no physical index, but up to three virtual indices. In this way, advantages of DMRG, in particular a low computational cost and a simple implementation of symmetries, are combined with advantages of TTNS, namely incorporating more entanglement. Our code is capable of simulating quantum chemical Hamiltonians, and we present several proof-of-principle calculations on LiF, N₂, and the bis(μ-oxo) and μ–η²:η² peroxo isomers of [Cu₂O₂]²⁺.

中文翻译：

T3NS：三腿树张量网络状态

我们提出了一种新的变分树张量网络状态（TTNS）ansatz，即三足树张量网络状态（T3NS）。物理张量散布着分支张量。物理张量具有一个物理索引，最多具有两个虚拟索引，例如在密度矩阵重归一化组（DMRG）的矩阵乘积状态（MPS）ansatz中。分支张量没有物理索引，但最多三个虚拟索引。这样，DMRG的优点（特别是低计算成本和简单的对称实现）与TTNS的优点相结合，即包含更多的纠缠。我们的代码能够模拟量子化学汉密尔顿的，我们本几个验证的原理上的LiF，N计算₂，以及双（μ-氧代）和μ-η ²：η ²[Cu ₂ O ₂ ] ^2+的过氧异构体。

更新日期：2018-02-26

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