Density matrix renormalization group (DMRG) for interacting spin chains and ladders

The density matrix renormalization group (DMRG) method generates the low-energy states of linear systems of N sites with a few degrees of freedom at each site by starting with a small system and adding sites step by step while keeping the dimension of the truncated Hilbert space constant. DMRG algorithms are adapted to open chains with inversion symmetry at the central site, to cyclic chains, to weakly coupled chains, and to low -T thermodynamics. The motivation is physical properties rather than energy accuracy. The algorithms are applied to the edge states of linear Heisenberg antiferromagnets with spin S= 1/2, the quantum phases of a frustrated spin-1/2 chain with an exchange between first and second neighbors, a spin-1/2 ladder with skewed rungs, and the spin-Peierls transitions of an organic and an inorganic crystal.