scholarly journals Matrix product operators, matrix product states, and ab initio density matrix renormalization group algorithms

2016 ◽  
Vol 145 (1) ◽  
pp. 014102 ◽  
Author(s):  
Garnet Kin-Lic Chan ◽  
Anna Keselman ◽  
Naoki Nakatani ◽  
Zhendong Li ◽  
Steven R. White
Keyword(s):  
Renormalization Group ◽  
Density Matrix ◽  
Ab Initio ◽  
Density Matrix Renormalization Group ◽  
Matrix Product ◽  
Matrix Product States ◽  
Density Matrix Renormalization

scholarly journals The density-matrix renormalization group: a short introduction

2011 ◽  
Vol 369 (1946) ◽  
pp. 2643-2661 ◽  
Author(s):  
Ulrich Schollwöck
Keyword(s):  
Renormalization Group ◽  
Density Matrix ◽  
Density Matrix Renormalization Group ◽  
Matrix Product ◽  
Lattice Systems ◽  
Density Matrix Renormalization ◽  
Statics And Dynamics ◽  
Network States ◽  
The Moment ◽  
Reduced Density

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.

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