Real-space quantum renormalization groups

Although originally thought to show great promise in solving quantum many-body problems on a lattice, numerical real-space renormalization-group techniques have had little success for such problems. We explore the nature of the difficulties involved by studying the applicaton of the method to the simple tight-binding model in one dimension. The standard approach fails dramatically for this model. We show that the key to successfully applying the renormalization-group technique lies in applying a variety of boundary conditions to a block in order to simulate the effect of neighboring blocks.