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

TL;DR

This paper introduces a new ab-initio many-body method for calculating the electronic structure of solids, utilizing localized Wannier functions and a multi-band Hamiltonian to incorporate many-body effects more rigorously.

Contribution

The paper presents a novel ab-initio approach that constructs a multi-band Hamiltonian from first principles, enabling more accurate many-body calculations in solids.

Findings

Hamiltonian derived from first principles for solids.

Method compatible with standard many-body techniques.

Explicit implementation in Hartree-Fock approximation.

Abstract

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