Variational solution of theT-matrix integral equation

Abstract

We present a variational solution of the T-matrix integral equation within a local approximation. This solution provides a simple form for the T matrix similar to Hubbard models but with the local interaction depending on momentum and frequency. By examining the ladder diagrams for irreducible polarizability, a connection between this interaction and the local-field factor is established. Based on the obtained solution, a form for the T-matrix contribution to the electron self-energy in addition to the GW term is proposed. In the case of the electron-hole multiple scattering, this form allows one to avoid double counting.

Theoretical study of quasiparticle inelastic lifetimes as applied to aluminum

“…3, the scattering amplitude should start from the third order in the screened interaction. 21,34 Such an additional term can be regarded as vertex corrections to the G 0 W 0 self-energy. As in the G 0 W⌳ case, a local approximation can be developed to solve the Bethe-Salpeter equation that describes the e-h scattering amplitude.…”

“…At that, to preserve all the advantages of the G 0 W 0 approximation, the integral over T can be considered as an additional term to the G 0 W 0 self-energy. 22,34 In this case, in order to avoid double counting, as in Ref. 3, the scattering amplitude should start from the third order in the screened interaction.…”

“…In Ref. 34, it has been done by using a variational approach yielding the amplitude T which in momentum space and in the case of a uniform system depends only on the four-momentum transfer along the electron-hole channel. As a result, the additional self-energy term ͓hereafter referred to as the T-matrix contribution and denoted by ⌺ T ͔ has the G 0 W 0 formula ͑7͒ with W 0 replaced by the scattering amplitude …”

Experimental time-resolved photoemission andab initiostudy of lifetimes of excited electrons in Mo and Rh

“…In this case, we additionally take into account third-and higher-order terms in the Hedin expansion of the selfenergy which constitute an infinite class of electron-hole ladder diagrams. 23,29 This allows us to consider the following scattering processes [see Fig. 3(b)].…”

“…20 The calculations by Zhukov et al 18 and Bacelar et al 19 showed that the evaluated lifetimes also strongly vary along the 4d-series following trends in electronic structure. The extension, GW + T , of the GW approximation by inclusion of multiple electron-hole scattering within a T-matrix approximation 21,22,23,24,25 results in the decrease of the GW lifetime value that brings theory and experiment to better agreement. 12,24,25 In this paper we perform TR-2PPE measurements of excited electron lifetimes in Mo and Rh and compare these results with the GW and GW + T calculated lifetimes.…”