# Nonperturbative theory of exchange and correlation in one-electron quasiparticle states

## Abstract

A nonperturbative argument is used to derive a one-electron Hamiltonian whose eigenfunctions are in one-to-one correspondence with electron or hole quasiparticles of an N-electron system. Nonlocal exchange is included exactly, and self-energy terms due to electronic correlation are included at the level of approximation of a given N-electron wave function. When parametrized by quasiparticle occupation numbers, this one-electron Hamiltonian is the functional derivative of an exact N-electron energy functional, as in the Landau theory of interacting fermion systems. The present nonperturbative derivation extends the Landau theory to ordered or localized systems for which many-body perturbation theory is not directly applicable. Analysis of the Bardeen-Cooper-Schrieffer (BCS) reduced Hamiltonian for superconductors leads to a temperature-dependent energy gap and a transition temperature in good agreement with the BCS theory, in a formalism that conserves the number of electrons. © 1986 The American Physical Society.