有效矩阵乘积算子的通有构造
Generic Construction of Efficient Matrix Product Operators
摘要：
矩阵乘积算子（MPO）是第二代密度矩阵重正化群（DMRG）算法的核心，该算法采用矩阵乘积状态语言。我们首先总结了MPO算法和单站点运营商表示的众所周知的事实。其次，我们介绍了三种压缩方法（重缩放SVD，解并行化和Delinearisation）的MPO和表明，它是可能的，以构建有效的表示任意运营商使用MPO算法和压缩。作为例子，我们构造了一个短程自旋链哈密顿量的幂，一个二维系统的复杂哈密顿量，作为原理的证明，从量子化学的长程四体哈密顿量。
英文摘要：
Matrix Product Operators (MPOs) are at the heart of the second-generation Density Matrix Renormalisation Group (DMRG) algorithm formulated in Matrix Product State language. We first summarise the widely known facts on MPO arithmetic and representations of single-site operators. Second, we introduce three compression methods (Rescaled SVD, Deparallelisation and Delinearisation) for MPOs and show that it is possible to construct efficient representations of arbitrary operators using MPO arithmetic and compression. As examples, we construct powers of a short-ranged spin-chain Hamiltonian, a complicated Hamiltonian of a two-dimensional system and, as proof of principle, the long-range four-body Hamiltonian from quantum chemistry.
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