Screening and Non-local Correlations in the Extended Hubbard Model from Self-Consistent Combined GW and Dynamical Mean Field Theory

TL;DR

This paper presents a self-consistent GW+DMFT approach to study the extended Hubbard model, revealing insights into phase transitions and non-local correlations with a numerically exact impurity solver.

Contribution

It introduces a numerically exact hybridization expansion continuous-time impurity solver within the GW+DMFT framework for the extended Hubbard model.

Findings

Mapped the phase diagram including metal-insulator and charge-ordered transitions.

Analyzed the frequency dependence of local interactions and its impact on spectral functions.

Provided a detailed comparison of GW+DMFT with other methods in the literature.

Abstract

We describe a recent implementation of the combined GW and dynamical mean field (DMFT) method "GW+DMFT" for the two-dimensional Hubbard model with on-site and nearest-neighbor repulsion. We clarify the relation of the GW+DMFT scheme to alternative approaches in the literature, and discuss the corresponding approximations to the free energy functional of the model. Furthermore, we describe a numerically exact technique for the self-consistent solution of the GW+DMFT equations, namely the hybridization expansion continuous-time algorithm for solving the dynamical impurity model that arises within the GW+DMFT scheme. We compute the low-temperature phase diagram of the extended Hubbard model, addressing the metal-insulator transition at small intersite interactions and the transition to a charge-ordered state for stronger intersite repulsions. Within the GW+DMFT framework, as in extended DMFT, the intersite repulsion translates into a frequency-dependence of the local effective interaction. We analyze this dependence by extracting a charateristic plasma frequency and show how it affects the local spectral function.