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Towards a novel approach for the calculation of many-body Green's functions

Giovanna Lani 1 
1 ST - Spectroscopie théorique
LSI - Laboratoire des Solides Irradiés
Abstract : In this work, a novel route to the calculation of the one particle Green's function (GF) has been developed. Its aim is to remedy to the shortcomings of other many-body approaches, e.g. the GW approximation (GWa), in treating strong effects of correlation in solids. The idea consists of solving a set of non-linear, differential, functional equations, which are pivotal to many-body perturbation theory. In a first instance, a so called 1-point model is employed (only one value for each time, spin, spatial variable is retained) and the set of equations reduces to a single algebraic equation, for which an explicit exact solution is obtained. The solution is used as a benchmark tool to analyze the performances of established many-body methods (e.g. different GW flavours), moreover alternative approximations are devised and for the most promising ones the generalization to their full functional form is discussed. The last part of the work deals with the generalization of the approach beyond the 1-point framework. First the frequency dependence of the GF is restored (while still retaining the 1-point approximation for the space and spin variables) and the set of equations is solved. It is shown that in such framework it is possible to recover the so-called cumulant expansion for the GF- an approximation which is beyond GW and provides accurate spectral functions for photo emission experiments. Finally, through an ansatz, a family of solution for the equations in their full functional form is obtained and routes to approximate the physical one, far beyond the present state-of-the-art, are proposed.
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Submitted on : Wednesday, February 8, 2012 - 4:08:35 PM
Last modification on : Sunday, June 26, 2022 - 12:33:33 AM
Long-term archiving on: : Thursday, November 22, 2012 - 11:45:18 AM


  • HAL Id : pastel-00667923, version 1



Giovanna Lani. Towards a novel approach for the calculation of many-body Green's functions. Strongly Correlated Electrons [cond-mat.str-el]. Ecole Polytechnique X, 2011. English. ⟨pastel-00667923⟩



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