论文标题
使用二分图理论最佳矩阵产品运营商最佳构造的通用自动方法
A General Automatic Method for Optimal Construction of Matrix Product Operators Using Bipartite Graph Theory
论文作者
论文摘要
构造矩阵产品运营商（MPO）是现代密度矩阵重新归一化组（DMRG）及其时间依赖性配方的核心。为了使DMRG在不同的哈密顿人描述的不同问题中方便使用，在这项工作中，我们提出了一种新的通用算法，以基于双方图理论构建具有含税形式的任意运算符的MPO。我们证明该方法具有以下优点：（i）自动变速箱，因为只需要操作员的定义； （ii）因此，它是符号的，因此没有任何数值误差； （iii）可以完全使用互补操作员技术，以使所产生的MPO在任何给定的自由度秩序上都是最佳的； （iv）可以完全使用系统的对称性来降低MPO的尺寸。为了证明新算法的有效性，构建了从典型的旋转玻璃模型和荷尔斯坦模型到更复杂的从头开始的电子汉密尔顿和六振动力场的MPO。发现对于以前的三种情况，我们的自动算法可以与文献中已经知道的最佳手工制作的算法相同。
Constructing matrix product operators (MPO) is at the core of the modern density matrix renormalization group (DMRG) and its time dependent formulation. For DMRG to be conveniently used in different problems described by different Hamiltonians, in this work we propose a new generic algorithm to construct the MPO of an arbitrary operator with a sum-of-products form based on the bipartite graph theory. We show that the method has the following advantages: (i) It is automatic in that only the definition of the operator is required; (ii) It is symbolic thus free of any numerical error; (iii) The complementary operator technique can be fully employed so that the resulting MPO is globally optimal for any given order of degrees of freedom; (iv) The symmetry of the system could be fully employed to reduce the dimension of MPO. To demonstrate the effectiveness of the new algorithm, the MPOs of Hamiltonians ranging from the prototypical spin-boson model and Holstein model to the more complicated ab initio electronic Hamiltonian and the anharmonic vibrational Hamiltonian with sextic force field are constructed. It is found that for the former three cases, our automatic algorithm can reproduce exactly the same MPOs as the optimally hand-crafted ones already known in the literature.
