Real-space numerical renormalization-group computation of photoemission spectra

Abstract

The concrete objective of this proposal is to compute accurately the photoemission spectrum of a simple metal slightly above the threshold energy. In this spectral region, the Anderson catastrophe forces the photoemission rate to grow without limit as the frequency approaches the threshold. Physically, the excess energy above the threshold promotes conduction electrons from levels below the Fermi energy to empty states above it. To describe accurately such particle-hole excitations, we will exploit a recently proposed, alternative formulation of the numerical renormalization-group (NRG) method. Dubbed eNRG, the new approach is defined in real space, in contrast with the logarithmic discretization in momentum space that is the signature of the NRG. While preserving the virtues of the NRG method, the eNRG approach is expected to offer more faithful description of the coupling between conduction bands and localized states. So far, the new method has been proven reliable in the computation of transport properties. Here, it will be extended to compute excitation properties. The proposal will be focused on a relatively simple model, which defines a problem at the undergraduate level. In this model, the photoemission excites an electron from a deep level to a free state with fixed energy, and the Hamiltonian acquires different forms in the initial and final states. The deep level is decoupled from the conduction band, but the positive charge at the deep level resulting from photoejection gives rise to a scattering potential in the final state. Since both the initial and the final Hamiltonians are quadratic, given a final state, it is relatively simple to compute the corresponding photoemission probability. The research will be focused on the development of a procedure to smooth the spectra resulting from the combination of contributions from numerous final states. (AU)