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 $\lambda$ that is smaller than the cutoff $\Lambda$ 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.

11 pages, final version, to be published in Phys. Rev. B

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