An ab-initio many-body method for electronic structure calculations of solids. I. Description of the method

摘要

We propose a new, alternative method for ab-initio calculations of theelectronic structure of solids, which has been specifically adapted to treatmany-body effects in a more rigorous way than many existing ab-initio methods.We start from a standard band-structure calculation for an effectiveone-particle Hamiltonian approximately describing the material of interest.This yields a suitable set of one-particle basis functions, from which welllocalized Wannier functions can be constructed using a method proposed byMarzari and Vanderbilt. Within this (minimal) basis of localized Wannierfunctions the matrix elements of the non-interacting (one-particle) Hamiltonianas well as the Coulomb matrix elements can be calculated. The result is amany-body Hamiltonian in second quantization with parameters determined fromfirst principles calculations for the material of interest. The Hamiltonian isin the form of a multi-band Hamiltonian in second quantization (a kind ofextended, multi-band Hubbard model) such that all the standard many-bodymethods can be applied. We explicitly show how this approach can be solved inthe simplest many-body approximation, the mean-field Hartree-Fock approximation(HFA), which takes into account exact exchange and corrects forself-interaction effects.