Generic construction of efficient matrix product operators
Generic construction of efficient matrix product operators
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DOI：
10.1103/physrevb.95.035129
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发表时间：
2016-11
影响因子：
3.7
通讯作者：
C. Hubig;I. McCulloch;Ulrich Schollwöck
中科院分区：
文献类型：
--
作者：
C. Hubig;I. McCulloch;Ulrich Schollwöck
矩阵乘积算子（MPO）是第二代密度矩阵重整化群（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的代表性的众所周知的事实。其次，我们介绍了三种压缩方法（重新缩放SVD，parallelization，和delinearization）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。
Matrix product operators (MPOs) are at the heart of the second-generation density matrix renormalization group (DMRG) algorithm formulated in matrix product state language. We first summarize the widely known facts on MPO arithmetic and representations of single-site operators. Second, we introduce three compression methods (rescaled SVD, deparallelization, and delinearization) 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.