Density-Matrix Renormalization: A New Numerical Method in Physics Lectures of a Seminar and Workshop Held at the Max-Planck-Institut für Physik komplexer Systeme Dresden, Germany, August 24th to September 18th, 1998

Theo Costi (auth.), Prof. Dr. Ingo Peschel, Dr. Matthias Kaulke, Dr. Xiaoqun Wang, Dr. Karen Hallberg (eds.)3540661298, 9783540661290

This book offers the first comprehensive account of the new method of density matrix renormalization. Recent years have seen enormous progress in the numerical treatment of low-dimensional quantum sytems. With this new technique, which selects a reduced set of basis states via density matrices, it has become possible to treat large systems with amazing accuracy. The method has been applied successfully to a variety of important one-dimensional problems such as spin chains, Kondo models, and correlated electron systems. Extensions to other systems and higher dimensions are currently being developed. The contributions to this book are written by leading experts in the field. The two parts contain an introduction to the subject and a review of physical applications. As a combination of advanced textbook and guide to current research the book should become a standard source for everyone interested in the topic.

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Table of contents :
Wilson’s numerical renormalization group….Pages 3-25
The Density Matrix Renormalization Group….Pages 27-66
Thermodynamic limit and matrix-product states….Pages 67-89
A recurrent variational approach….Pages 91-125
Transfer-matrix approach to classical systems….Pages 127-148
Quantum transfer-matrix and momentum-space DMRG….Pages 149-172
Calculation of dynamical properties….Pages 173-194
Properties of the hubbard chain….Pages 197-209
Soliton bound-states in dimerized spin chains….Pages 211-220
Haldane phase, impurity effects and spin ladders….Pages 221-230
Spin chain properties….Pages 231-236
Electronic structure using DMRG….Pages 237-246
Symmetrized DMRG method for conjugated polymers….Pages 247-260
Conjugated one-dimensional semiconductors….Pages 261-269
Strongly correlated complex systems….Pages 271-278
Non-hermitian problems and some other aspects….Pages 279-285
Walls, wetting and surface criticality….Pages 287-294
Critical two-dimensional ising films with fields….Pages 295-302
One-dimensional Kondo lattices….Pages 303-310
Impurities in spin chains….Pages 311-320
Thermodynamics of ferrimagnets….Pages 321-328
Thermodynamics of metallic kondo lattices….Pages 329-336
Methods for electron-phonon systems….Pages 337-344
Disordered one-dimensional fermi systems….Pages 345-355