With the goal of enabling more realistic simulations of nonequilibrium states in correlated electron systems, we have developed new simulation approaches based on cluster extensions of DMFT, the combination of the GW method and DMFT, and on combinations of the two-particle self-consistent approach (TPSC) and DMFT. The GW method captures weak correlation phenomena and the effect of nonlocal charge fluctuations (dynamical screening). It is based on diagrammatic perturbation theory and can be combined in a consistent way with the DMFT formalism, which captures strong local correlations.
Our ab-initio GW+DMFT scheme is a multi-scale approach that involves a separation into different orbital subspaces, which are treated with different approximations: the states at high energy are treated within single-shot GW, those at intermediate energy within self-consistent GW, and the most strongly correlated low-energy states within selfconsistent GW+DMFT. Numerous tests showed that this scheme, which is free of ad-hoc parameters, correctly reproduces the electronic structure of correlated materials. TPSC is a weak-coupling approach which provides a consistent description of single particle quantities (self-energies) and two-particle quantities (vertex functions). It has been shown to provide accurate results for moderately correlated systems, and its recent combination with DMFT allows to extend this method to the strongly correlated regime.
An important achievement of Modmat is the implementation of nonequilibrium generalizations of the GW+DMFT and TPSC(+DMFT) methods. GW+DMFT involves the self-consistent calculation of a dynamically screened interaction. We have implemented this method for the d-p model for charge transfer insulators, which involves weakly correlated p electrons and strongly correlated d electrons. The proper implementation of the light-matter coupling in such multi-orbital systems is nontrivial and has been worked out. In the case of TPSC(+DMFT) the nonequilibrium formalism has been implemented and systematically benchmarked for the two- and three-dimensional single-band Hubbard model, while generalizations to multi-orbital systems are still ongoing.
We have also implemented cluster extensions of nonequilibrium DMFT. These calculations capture strong short-ranged correlations, and have for example been used to simulate exciton formation resulting from non-local Coulomb interactions. To explore nonequilibrium effects in weakly correlated materials, we have furthermore employed weak-coupling perturbative methods, and simulations based on the so-called Generalized Kadanoff-Baym approximation. This approximation allows to study relatively large lattice systems up to timescales that are relevant for electronic processes.
Powerful new methods and codes should be made available to the broader scientific community. We have published the open source software NESSi (nonequilibrium systems simulation package),
http://nessi.tuxfamily.org/index.html(s’ouvre dans une nouvelle fenêtre) which enables accurate and efficient calculations with nonequilibrium Green's functions. This software provides the basic functionalities for most of our method development projects and the availability of the Nessi library will substantially lower the barrier for other research groups who wish to perform Green's function based nonequilibrium simulations.
