Realistic theory of electronic correlations in nanoscopic systems

TL;DR

This paper reviews advanced theoretical methods for accurately modeling electronic and magnetic properties of nanostructures with strong correlations, emphasizing the integration of density functional theory with dynamical mean field theory and addressing non-local interactions.

Contribution

It introduces a flexible DFT-DMFT interface suitable for complex correlated nanostructures and discusses recent developments in quantum Monte Carlo, exact diagonalization, and non-local correlation techniques.

Findings

Demonstrates how Hubbard U and Hund's J influence charge and spin fluctuations.

Shows the impact of dimensionality and environment coupling on correlation phenomena.

Addresses challenges of non-local interactions in low-dimensional systems.

Abstract

Nanostructures with open shell transition metal or molecular constituents host often strong electronic correlations and are highly sensitive to atomistic material details. This tutorial review discusses method developments and applications of theoretical approaches for the realistic description of the electronic and magnetic properties of nanostructures with correlated electrons. First, the implementation of a flexible interface between density functional theory and a variant of dynamical mean field theory (DMFT) highly suitable for the simulation of complex correlated structures is explained and illustrated. On the DMFT side, this interface is largely based on recent developments of quantum Monte Carlo and exact diagonalization techniques allowing for efficient descriptions of general four fermion Coulomb interactions, reduced symmetries and spin-orbit coupling, which are explained here. With the examples of the Cr (001) surfaces, magnetic adatoms, and molecular systems it is shown how the interplay of Hubbard U and Hund's J determines charge and spin fluctuations and how these interactions drive different sorts of correlation effects in nanosystems. Non-local interactions and correlations present a particular challenge for the theory of low dimensional systems. We present our method developments addressing these two challenges, i.e., advancements of the dynamical vertex approximation and a combination of the constrained random phase approximation with continuum medium theories. We demonstrate how non-local interaction and correlation phenomena are controlled not only by dimensionality but also by coupling to the environment which is typically important for determining the physics of nanosystems.