Renormalization approach to many-particle systems

Abstract

This paper presents a renormalization approach to many-particle systems. By starting from a bare Hamiltonian $\mathcal{H}={\mathcal{H}}_{0}+{\mathcal{H}}_{1}$ with an unperturbed part ${\mathcal{H}}_{0}$ and a perturbation ${\mathcal{H}}_{1},$ we define an effective Hamiltonian which has a band-diagonal shape with respect to the eigenbasis of ${\mathcal{H}}_{0}.$ This means that all transition matrix elements are suppressed which have energy differences larger than a given cutoff $\ensuremath{\lambda}$ that is smaller than the cutoff $\ensuremath{\Lambda}$ of the original Hamiltonian. This property resembles a recent flow equation approach on the basis of continuous unitary transformations. For demonstration of the method we discuss an exact solvable model, as well as the Anderson-lattice model where the well-known quasiparticle behavior of heavy fermions is derived.