# Realistic many-body approaches to materials with strong nonlocal correlations

## TL;DR

This paper discusses advanced many-body computational methods that incorporate both local and nonlocal electronic correlations to better understand complex transition-metal materials.

## Contribution

It introduces combined approaches integrating dynamical mean-field theory with band-structure methods and addresses nonlocal correlations beyond mean-field.

## Key findings

- Successful integration of DMFT with band-structure methods
- Demonstrated importance of nonlocal correlations in material properties
- Outlined future directions for methodological improvements

## Abstract

Many of the fascinating and unconventional properties of several transition-metal compounds with partially filled d-shells are due to strong electronic correlations. While local correlations are in principle treated exactly within the frame of the dynamical mean-field theory, there are two major and interlinked routes for important further methodical advances: On the one hand, there is a strong need for methods being able to describe material-specific aspects, i.e., methods combining the DMFT with modern band-structure theory, and, on the other hand, nonlocal correlations beyond the mean-field paradigm must be accounted for. Referring to several concrete example systems, we argue why these two routes are worth pursuing and how they can be combined, we describe several related methodical developments and present respective results, and we discuss possible ways to overcome remaining obstacles.