Department of Physics, Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, University of Munich, Theresienstrasse 37, 80333 Munich, Germany.
Philos Trans A Math Phys Eng Sci. 2011 Jul 13;369(1946):2643-61. doi: 10.1098/rsta.2010.0382.
The density-matrix renormalization group (DMRG) method has established itself over the last decade as the leading method for the simulation of the statics and dynamics of one-dimensional strongly correlated quantum lattice systems. The DMRG is a method that shares features of a renormalization group procedure (which here generates a flow in the space of reduced density operators) and of a variational method that operates on a highly interesting class of quantum states, so-called matrix product states (MPSs). The DMRG method is presented here entirely in the MPS language. While the DMRG generally fails in larger two-dimensional systems, the MPS picture suggests a straightforward generalization to higher dimensions in the framework of tensor network states. The resulting algorithms, however, suffer from difficulties absent in one dimension, apart from a much more unfavourable efficiency, such that their ultimate success remains far from clear at the moment.
密度矩阵重整化群（DMRG）方法在过去十年中已确立为模拟一维强关联量子格子系统的静态和动态的主要方法。DMRG 是一种方法，它具有重整化群程序（在此生成约化密度算子空间中的流）和变分方法的特征，该变分方法作用于一类非常有趣的量子态，即所谓的矩阵乘积态（MPS）。DMRG 方法在此完全用 MPS 语言表示。尽管 DMRG 通常在较大的二维系统中失败，但 MPS 图像表明在张量网络态的框架中可以直接推广到更高的维度。然而，除了效率更差之外，由此产生的算法还存在一维中不存在的困难，因此它们的最终成功目前还远不清楚。
