Flow‐equations for Hamiltonians

Abstract

Flow‐equations are introduced in order to bring Hamiltonians closer to diagonalization. It is characteristic for these equations that matrix‐elements between degenerate or almost degenerate states do not decay or decay very slowly. In order to understand different types of physical systems in this framework it is probably necessary to classify various types of these degeneracies and to investigate the corresponding physical behavior. In general these equations generate many‐particle interactions. However, for an n‐orbital model the equations for the two‐particle interaction are closed in the limit of large n. Solutions of these equations for a one‐dimensional model are considered. There appear convergency problems, which are removed, if instead of diagonalization only a block‐diagonalization into blocks with the same number of quasiparticles is performed.