Abstract
In this chapter I will introduce the basic Density Matrix Renormalization Group (DMRG) algorithms for calculating ground states in quantum lattice many-body systems using the one-dimensional spin- 1 Heisenberg model as illustration. I will attempt to present these methods in a manner which combines the advantages of both the traditional formulation in terms of renormalized blocks and superblocks and the new description based on matrix-product states. The latter description is physically more intuitive but the former description is more appropriate for writing an actual DMRG program. Pedagogical introductions to DMRG which closely follow the original formulation are available in [2, 1]. The conceptual background of DMRG and matrix-product states is discussed in the previous chapter and should be read before. Extensions of the basic DMRG algorithms are presented in the chapters that follow this one.
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