The density-matrix renormalization group in the age of matrix product states
The density-matrix renormalization group in the age of matrix product states
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DOI：
10.1016/j.aop.2010.09.012
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发表时间：
2011-01-01
影响因子：
3
通讯作者：
Schollwoeck, Ulrich
中科院分区：
文献类型：
--
作者：
Schollwoeck, Ulrich
密度矩阵重整化群方法（DMRG）在过去的十年中已经成为模拟一维强关联量子晶格系统静态和动态的主要方法。在该方法的进一步发展中，DMRG对一类非常有趣的量子态（所谓的矩阵乘积态（MPS））进行操作的认识，使人们能够更深入地了解DMRG方法的内部结构，其进一步的潜力及其局限性。在这篇论文中。我想用MPS语言详细阐述当前的DMRG思想，以使DMRG算法家族在MPS术语中的明智实现透明化。然后，我继续讨论一些可能富有成效的进一步算法开发的方向：虽然DMRG现在是一个非常成熟的方法，但我仍然看到进一步改进的潜力，最近引入的一些算法就是例证。(C)2010年由Elsevier Inc.出版
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. (C) 2010 Published by Elsevier Inc.