scholarly journals Matrix-product-state comparison of the numerical renormalization group and the variational formulation of the density-matrix renormalization group

2008 ◽  
Vol 78 (3) ◽  
Author(s):  
Hamed Saberi ◽  
Andreas Weichselbaum ◽  
Jan von Delft
Keyword(s):  
Renormalization Group ◽  
Density Matrix ◽  
Variational Formulation ◽  
Density Matrix Renormalization Group ◽  
Matrix Product ◽  
Product State ◽  
Numerical Renormalization Group ◽  
Density Matrix Renormalization ◽  
Matrix Product State

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.

RECENT PROGRESS IN THE DENSITY-MATRIX RENORMALIZATION GROUP

2007 ◽  
Vol 21 (13n14) ◽  
pp. 2564-2575 ◽  
Author(s):  
ULRICH SCHOLLWÖCK
Keyword(s):  
Renormalization Group ◽  
Density Matrix ◽  
Quantum Systems ◽  
Density Matrix Renormalization Group ◽  
Strongly Correlated ◽  
Powerful Method ◽  
Numerical Renormalization Group ◽  
One Dimensional ◽  
Density Matrix Renormalization ◽  
Quantum Impurity

Over the last decade, the density-matrix renormalization group (DMRG) has emerged as the most powerful method for the simulation of strongly correlated one-dimensional (1D) quantum systems. Input from quantum information has allowed to trace the method's performance to the entanglement properties of quantum states, revealing why it works so well in 1D and not so well in 2D; it has allowed to devise algorithms for time-dependent quantum systems and, by clarifying the link between DMRG and Wilson's numerical renormalization group (NRG), for quantum impurity systems.

Sign in / Sign up

Export Citation Format

Share Document