Flow equations for Hamiltonians

A recently developed method to diagonalize or block-diagonalize Hamiltonians by means of an appropriate continuous unitary transformation is reviewed. The main aspects will be discussed: (i) Elimination of off-diagonal matrix elements at different energy scales and (ii) problems and advantages of this method. Two applications in condensed matter physics are given as examples: the interaction of an n-orbital model of fermions in the limit of large n is brought to block-diagonal form, and the generation of the effective attractive two-electron interaction due to the elimination of electron–phonon interaction is given. The advantage of this method in particular in comparison with conventional perturbation theory is pointed out.