scholarly journals Comment on “Equivalence of the variational matrix product method and the density matrix renormalization group applied to spin chains” by J. Dukelsky et al.

2003 ◽  
Vol 61 (1) ◽  
pp. 138-139
Author(s):  
I. P McCulloch ◽  
M Gulácsi
Keyword(s):  
Renormalization Group ◽  
Density Matrix ◽  
Spin Chains ◽  
Density Matrix Renormalization Group ◽  
Matrix Product ◽  
Variational Matrix ◽  
Density Matrix Renormalization ◽  
Product Method

RENORMALIZATION-GROUP INVESTIGATION OF THE S = 1 RANDOM ANTIFERROMAGNETIC HEISENBERG CHAIN

2006 ◽  
Vol 17 (12) ◽  
pp. 1739-1753 ◽  
Author(s):  
PÉTER LAJKÓ
Keyword(s):  
Phase Diagram ◽  
Renormalization Group ◽  
Density Matrix ◽  
Energy Scale ◽  
Quantum Spin ◽  
Spin Chains ◽  
Density Matrix Renormalization Group ◽  
Heisenberg Chain ◽  
Quantum Spin Chains ◽  
Density Matrix Renormalization

We introduce variants of the Ma-Dasgupta renormalization-group (RG) approach for random quantum spin chains, in which the energy-scale is reduced by decimation built on either perturbative or non-perturbative principles. In one non-perturbative version of the method, we require the exact invariance of the lowest gaps, while in a second class of perturbative Ma-Dasgupta techniques, different decimation rules are utilized. For the S = 1 random antiferromagnetic Heisenberg chain, both type of methods provide the same type of disorder dependent phase diagram, which is in agreement with density-matrix renormalization-group calculations and previous studies.

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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