Downfolded Self-Energy of Many-Electron Systems

TL;DR

This paper develops a formalism to derive an effective self-energy for electrons in a subspace of the full Hilbert space, facilitating modeling of strongly correlated materials and enabling first-principles calculations focused on key correlated subspaces.

Contribution

It introduces a general framework for deriving frequency-dependent effective interactions and self-energies for selected subspaces within many-electron systems.

Findings

Provides a method to obtain effective self-energy in a reduced subspace.

Delivers a way to compute the Hubbard U from first principles.

Framework applicable to strongly correlated materials.

Abstract

Starting from the full many-body Hamiltonian of interacting electrons the effective self-energy acting on electrons residing in a subspace of the full Hilbert space is derived. This subspace may correspond to, for example, partially filled narrow bands, which often characterize strongly correlated materials. The formalism delivers naturally the frequency-dependent effective interaction (the Hubbard U) and provides a general framework for constructing theoretical models based on the Green function language. It also furnishes a general scheme for first-principles calculations of complex systems in which the main correlation effects are concentrated on a small subspace of the full Hilbert space.