contrast our method is suited to calculate the flow-behaviour of the system, even analytically, although the main advantage by comparison with TMRG is the simple structure of our RG scheme. This makes it an easy task to apply it to a great variety of physical models.

The rest of this article is organized as follows: In the next section we review the key idea of DMRG shortly. We begin by introducing the standard concepts of the real-space RG method in the language of spin chains in the way it was originally proposed. In section III we present a rigorous formulation of a real-space RG transformation. Each single block within the blocked chain is enlarged by an additional space, the auxiliary space. A single block together with its auxiliary space is called a superblock for which a real-space RG transformation is defined by integrating out the small spatial structure. Constructing a global RG transformation for the complete quantum system from concatenation of the local superblock RG transformations leads to the definition of exact and perfect RG transformations. In section V we give some final remarks including the relation to previous approaches in this direction. Applications in terms of this new formulation 