arXiv:cond-mat/9405034 · Journal of Physics A Mathematical and General

Flow equations for the Anderson Hamiltonian

Stefan K. Kehrein, Andreas Mielke

Published Jun 21, 1994• 36 citations

Abstract

Using a continuous unitary transformation recently proposed by Wegner \cite{Wegner} together with an approximation that neglects irrelevant contributions, we obtain flow equations for Hamiltonians. These flow equations yield a diagonal or almost diagonal Hamiltonian. As an example we investigate the Anderson Hamiltonian for dilute magnetic alloys. We study the different fixed points of the flow equations and the corresponding relevant, marginal or irrelevant contributions. Our results are consistent with results obtained by a numerical renormalization group method, but our approach is considerably simpler.

DOI: 10.1088/0305-4470/27/12/030

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arXiv:cond-mat/9405034 · Journal of Physics A Mathematical and General

Flow equations for the Anderson Hamiltonian

Stefan K. Kehrein, Andreas Mielke

Published Jun 21, 1994• 36 citations

arXiv HTML PDF

Abstract

DOI: 10.1088/0305-4470/27/12/030

Related papers

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We derive Hamiltonian flow equations giving the evolution of the Lipkin Hamiltonian to a diagonal form using continuous unitary transformations. To close the system of flow equations, we present two different schemes. First we linearize an operator with three pairs of creation and destruction operators by reducing it to the $z$ component of the quasi spin. We obtain the well known RPA-result in the limit of large particle number. In the second scheme we introduce a new operator which improves the resulting spectrum considerably especially for few particles.We derive Hamiltonian flow equations giving the evolution of the Lipkin Hamiltonian to a diagonal form using continuous unitary transformations. To close the system of flow equations, we present two different schemes. First we linearize an operator with three pairs of creation and destruction operators by reducing it to the $z$ component of the quasi spin. We obtain the well known RPA-result in the limit of large particle number. In the second scheme we introduce a new operator which improves the resulting spectrum considerably especially for few particles.

Jan 1, 199811 citations

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.

\alpha

. We derive the flow equations, and the evolution of single-particle operators. The flow equation reveals the delocalized nature of the states for

\alpha 1/2

, we present a strong-bond renormalization group structure based on iterating the three-site clusters, where we solve the flow equations perturbatively. This renormalization group approach allows us to probe the critical point

\left(\alpha=1\right)

. This method correctly reproduces the critical level-spacing statistics, and the fractal dimensionality of the eigenfunctions.

z

component of the quasi spin. We obtain the well known RPA-result in the limit of large particle number. In the second scheme we introduce a new operator which improves the resulting spectrum considerably especially for few particles.