Renormalization approach to many-particle systems

TL;DR

This paper introduces a renormalization method for many-particle systems that simplifies the Hamiltonian by suppressing large energy transitions, demonstrated on solvable and heavy fermion models.

Contribution

It develops a renormalization approach that produces a band-diagonal effective Hamiltonian, akin to flow equation methods, applied to complex many-particle models.

Findings

Effective Hamiltonian with suppressed large energy transitions.

Application to an exactly solvable model.

Derivation of quasiparticle behavior in heavy fermions.

Abstract

This paper presents a renormalization approach to many-particle systems. By starting from a bare Hamiltonian ${\cal H}= {\cal H}_0 +{\cal H}_1$ with an unperturbed part ${\cal H}_0$ and a perturbation ${\cal H}_1$,we define an effective Hamiltonian which has a band-diagonal shape with respect to the eigenbasis of ${\cal H}_0$. 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.