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Nonequilibrium dynamical mean-field theory: From models to materials

Periodic Reporting for period 3 - MODMAT (Nonequilibrium dynamical mean-field theory: From models to materials)

Reporting period: 2020-05-01 to 2021-10-31

The aim of the Modmat project is to develop theoretical and computational tools which enable a quantitative description of correlated electron systems driven by strong laser fields. Several recent experiments have demonstrated remarkable phenomena occurring in photo-excited solids. These phenomena range from light-induced insulator-to-metal transitions and apparent light-induced room-temperature superconductivity to the switching of materials into long-lived metastable states with properties different from those of any know equilibrium phase. All these experiments involve complex materials with strong electronic correlations and competing low-energy states. Already an accurate description of the equilibrium phases of these materials poses great challenges, and the theoretical understanding of the nonequilibrium phenomena which can occur in such systems in response to strong perturbations is currently very limited.

Significant progress has been made at the level of simple model systems with the development of nonequilibrium dynamical mean field theory (DMFT). This method allows to treat strong local correlations, and it captures the nonequilibrium states induced by strong electric fields. Simple model calculations however miss important phenomena, such as modifications in the screening properties and hence in the effective interactions between electrons. They are also not material specific and thus can only provide qualitative insights into phenomena observed in experiments. Within Modmat, we are developing extensions of nonequilibrium DMFT which allow to overcome some of these limitations, and which will enable ab-initio simulations of nonequilibrium phenomena in correlated solids. With these tools it should not only become possible to quantitatively reproduce the electronic response to laser fields, but also to predict phenomena and their characteristic timescales for specific materials.

Ultimately, many technological advances are related to the improvement and control of material properties. Extending our knowledge and understanding to nonequilibrium states of matter will provide a basis for developing new devices with new or improved functionalities.
With the goal of realizing material-specific simulations of nonequilibrium states, we are developing a new simulation approach based on the combination of the GW method and dynamical mean field theory (DMFT). The GW method has been built into standard ab-initio codes and 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. In the context of equilibrium simulations, we have developed a full ab-initio GW+DMFT scheme, which 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. The multi-scale approach is physically motivated and makes this scheme computationally feasible. First tests show that the method, which is entirely free of ad-hoc parameters, correctly reproduces the electronic structure of different materials.

In parallel, we have been developing a nonequilibrium version of GW+DMFT. First, this was achieved at the level of a single-band Hubbard model, which already required significant extensions beyond the previous state-of-the-art. In particular, GW+DMFT captures dynamical screening effects and involves the self-consistent calculation of a polarization function and effective interaction. The machinery which allows to deal with this additional complexity had to be developed and implemented. A big step towards the final goal was the subsequent extension of the nonequilibrium GW+DMFT method to the so-called d-p model for charge transfer insulators. This model involves a multi-band set-up with weakly correlated p electrons and strongly correlated d electrons, and thus requires a multi-scale treatment similar to the one used in realistic materials simulations. Also, the light-matter coupling in such multi-orbital systems is more complex than in a single-band model, so that the proper implementation of electric field excitations required a significant effort. From the GW+DMFT simulations of the d-p model, it will be a relatively small step to the realization of proper ab-initio simulations. This step essentially involves the use of bare propagators and bare interactions derived from the equilibrium scheme that we have developed in parallel.

While GW+DMFT captures nonlocal charge fluctuations, it does not accurately describe nonlocal spin fluctuations. The latter are important in certain correlated materials, for example cuprates. To develop an understanding of the interplay between spin and charge dynamics in nonequilibrium states, we have also been working on different types of extensions of DMFT. One of these approaches is the nonequilibrium extended DMFT for the t-J model, which is a model with nonlocal spin interactions. The other approach is a cluster extension of DMFT. Both of these have been successfully used to study properties of photo-excited Mott systems which cannot be described in GW+DMFT. We have also used the cluster scheme to simulate exciton formation resulting from non-local Coulomb interactions. Ultimately, it would be very nice to combine the complementary strengths of (nonequilibrium) GW+DMFT and (nonequilibrium) cluster DMFT into a scheme that properly describes short-range and long-range correlations.

To complement our portfolio of simulation methods for correlated lattice systems, and to explore nonequilibrium effects in weakly correlated materials (e. g. semi-conductors and transition metal dichalcogenides), we have also invested some time into the development of 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.

Eventually, powerful new methods and codes should be made available to the broader scientific community. As an important first step, we have published the open source software NESSi (nonequilibrium systems simulation package), 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 this software will substantially lower the barrier for other research groups who wish to perform Green's function based nonequilibrium simulations.
Modmat is a project focusing on the development of new methods for nonequilibrium materials simulations, which all go beyond the previous state-of-the-art. In particular, equilibrium and nonequilibrium GW+DMFT represents a significant step beyond the simple DMFT approach because it involves a fully self-consistent description of correlation and screening effects in the solid. It is a fully parameter-free ab-initio approach, and in fact the first true ab-inito approach for strongly correlated solids. Also our work on nonequilibrium cluster extensions of DMFT represents a significant methodological advance.

In the second half of the Modmat project, we will try to apply the newly developed machinery to a broad range of problems, both at the model level and with the goal of making contact to experiments. We expect that these results will provide a good understanding of how electronic correlations influence the relaxation pathways and transient states in photo-excited solids. By studying models of increasing complexity, we also hope to reveal some of the mechanisms which can lead to the trapping of laser-driven systems in long-lived nonthermal states.

Currently, the simulations of complex systems are limited to relatively short times (fast dynamics). On the technical side, one of the main challenges is to extend the time window which the simulations can cover. The most promising strategy here is the implementation of truncation schemes which reduce the memory demand of nonequilibrium Green’s function simulations.