The density-matrix renormalization group method (DMRG) 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. In
the further development of the method, the realization that DMRG operates on a
highly interesting class of quantum states, so-called matrix product states
(MPS), has allowed a much deeper understanding of the inner structure of the
DMRG method, its further potential and its limitations. In this paper, I want
to give a detailed exposition of current DMRG thinking in the MPS language in
order to make the advisable implementation of the family of DMRG algorithms in
exclusively MPS terms transparent. I then move on to discuss some directions of
potentially fruitful further algorithmic development: while DMRG is a very
mature method by now, I still see potential for further improvements, as
exemplified by a number of recently introduced algorithms.

本篇研究论文以 MPS 语言详细阐述了当前 DMRG 思想，以期实现 DMRG 算法族在纯 MPS 术语下的可行性实现，并讨论了一些潜在的有益算法发展方向，最终目标是使 DMRG 方法得到进一步改进。