A Renormalized-Hamiltonian-Flow Approach to Eigenenergies and Eigenfunctions*

Abstract

Abstract We introduce a decimation scheme of constructing renormalized Hamiltonian flows, which is useful in the study of properties of energy eigenfunctions, such as localization, as well as in approximate calculation of eigenenergies. The method is based on a generalized Brillouin-Wigner perturbation theory. Each flow is specific for a given energy and, at each step of the flow, a finite subspace of the Hilbert space is decimated in order to obtain a renormalized Hamiltonian for the next step. Eigenenergies of the original Hamiltonian appear as unstable fixed points of renormalized flows. Numerical illustration of the method is given in the Wigner-band random-matrix model.