# Merging GW with DMFT and non-local correlations beyond

## TL;DR

This paper reviews advanced electronic structure methods beyond DFT and DMFT, including GW, GW+DMFT, and DΓA, highlighting their capabilities in capturing non-local correlations and quantum critical phenomena, with applications to SrVO3.

## Contribution

It introduces and compares three cutting-edge methods that incorporate non-local correlations beyond traditional approaches, emphasizing their implementation and results for SrVO3.

## Key findings

- GW, GW+DMFT, and DΓA successfully capture non-local correlations.
- The methods provide insights into quantum critical behavior.
- Benchmark results for SrVO3 demonstrate the effectiveness of these approaches.

## Abstract

We review recent developments in electronic structure calculations that go beyond state-of-the-art methods such as density functional theory (DFT) and dynamical mean field theory (DMFT). Specifically, we discuss the following methods: GW as implemented in the Vienna {\it ab initio} simulation package (VASP) with the self energy on the imaginary frequency axis, GW+DMFT, and ab initio dynamical vertex approximation (D$\Gamma$A). The latter includes the physics of GW, DMFT and non-local correlations beyond, and allows for calculating (quantum) critical exponents. We present results obtained by the three methods with a focus on the benchmark material SrVO$_3$.