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

Ingo Peschel, Xiaoqun Wang, Matthias Kaulke, Karen Hallberg (Herausgeber)

Buch | Hardcover

XVI, 355 Seiten

1999 | 1999
Springer Berlin (Verlag)
978-3-540-66129-0 (ISBN)

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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. TOC:Introductory Lectures: Wilson's Numerical Renormalization Group; The Density Matrix Renormalization Group; Thermodynamic Limit and Matrix-Product States; A Recurrent Variational Approach; Transfer-Matrix Approach to Classical Systems; Transfer-Matrix and Momentum-Space DMRG; Calculation of Dynamical Properties.- Physical Applications: Chains and Ladders; Molecules and Polymers; Classical Statistical Physics; Thermodynamic Properties; Phonons and Disorder.

Wilson's numerical renormalization group.- The Density Matrix Renormalization Group.- Thermodynamic limit and matrix-product states.- A recurrent variational approach.- Transfer-matrix approach to classical systems.- Quantum transfer-matrix and momentum-space DMRG.- Calculation of dynamical properties.- Properties of the hubbard chain.- Soliton bound-states in dimerized spin chains.- Haldane phase, impurity effects and spin ladders.- Spin chain properties.- Electronic structure using DMRG.- Symmetrized DMRG method for conjugated polymers.- Conjugated one-dimensional semiconductors.- Strongly correlated complex systems.- Non-hermitian problems and some other aspects.- Walls, wetting and surface criticality.- Critical two-dimensional ising films with fields.- One-dimensional Kondo lattices.- Impurities in spin chains.- Thermodynamics of ferrimagnets.- Thermodynamics of metallic kondo lattices.- Methods for electron-phonon systems.- Disordered one-dimensional fermi systems.

Erscheint lt. Verlag	21.6.1999
Reihe/Serie	Lecture Notes in Physics
Zusatzinfo	XVI, 355 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	644 g
Themenwelt	Naturwissenschaften ► Physik / Astronomie ► Allgemeines / Lexika
	Naturwissenschaften ► Physik / Astronomie ► Festkörperphysik
	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
	Naturwissenschaften ► Physik / Astronomie ► Thermodynamik
Schlagworte	density • Dynamics • electron • Fields • Mathematische Physik • Molecule • numerical method • Physics • Polymer • renormalization • Renormalization Group • semiconductor • Soliton • Spin • Statistical Physics • thermodynamics
ISBN-10	3-540-66129-8 / 3540661298
ISBN-13	978-3-540-66129-0 / 9783540661290
Zustand	Neuware