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, 1998Ingo Peschel 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. |
Contents
Wilsons Numerical Renormalization Group | 3 |
The Density Matrix Renormalization Group | 27 |
Thermodynamic Limit and MatrixProduct States | 67 |
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accuracy ansatz basis Bethe Ansatz bond boundary conditions Chap configuration convergence correlation function correlation length corresponding coupling defined density matrix discussed DMRG calculations DMRG method DMRG results doping dynamic eigenstates eigenvalues eigenvectors electrons error excitations fermion ferromagnetic finite finite-size finite-system algorithm fixed point ground ground-state energy H₁ Haldane Hamiltonian Heisenberg model Hilbert space Hubbard model impurity model interaction iteration Kondo model largest eigenvalue lattice Lett low-energy lowest magnetic matrix elements matrix product Nishino obtained one-dimensional open boundary operators optimal orbitals orthlet parameters particle phonon Phys plaquette problem procedure properties pseudo-site quantum Ramasesha reduced density matrix renormalization group representation S.R. White Sect shown in Fig singlet soliton spectral spectrum spin chains spin gap subspace superblock symmetry system block t-J model target temperature thermodynamic limit TMRG total spin transfer matrix triplet Trotter truncation values variational vector wavefunction Xiang