Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
2010-08-20
Annals of Physics 326, 96 (2011)
Physics
Condensed Matter
Strongly Correlated Electrons
118 pages, 63 figures; minor changes in this final version: typos eliminated and a few references added
Scientific paper
10.1016/j.aop.2010.09.012
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.
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