Periodic Reporting for period 4 - MODMAT (Nonequilibrium dynamical mean-field theory: From models to materials)
Reporting period: 2021-11-01 to 2023-04-30
The aim of the Modmat project was to develop computational tools which enable a description of correlated electron systems driven by laser fields. Several recent experiments have demonstrated remarkable phenomena occurring in photo-excited solids. These 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, and the theoretical understanding of the nonequilibrium phenomena which 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 or multiorbital effects. They are also not material specific and thus can only provide qualitative insights into phenomena observed in experiments. Within Modmat, we developed extensions of nonequilibrium DMFT which allow to overcome some of these limitations, and which enable more realistic studies of nonequilibrium phenomena in correlated solids.
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 devices with new functionalities.
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 or multiorbital effects. They are also not material specific and thus can only provide qualitative insights into phenomena observed in experiments. Within Modmat, we developed extensions of nonequilibrium DMFT which allow to overcome some of these limitations, and which enable more realistic studies of nonequilibrium phenomena in correlated solids.
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 devices with new functionalities.
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 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.
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 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.
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, 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. Also our work on nonequilibrium TPSC(+DMFT) represents a significant methodological advance. We have furthermore developed truncation schemes which reduce the memory demand of nonequilibrium Green’s function simulations. This approach enables simulations of single-orbital systems up to several thousand hopping times.
On the conceptual side, the Modmat project has produced numerous insights into mechanisms which can stabilize interesting nonthermal states, including eta-pairing states and nonthermal excitonic or spin/orbital orders. We also demonstrated that chiral superconducting states can be induced by photo-doping Mott insulators on geometrically frustrated lattices. In connection with experiments, an important step forward has been the clarification of the insulating nature of the correlated insulator 1T-TaS2, and its response to photo-doping.
When new methods are developed, it is important to benchmark them against available results. However, for nonequilibrium states of strongly correlated lattice systems, few established methods exist. We therefore benchmarked nonequilibrium DMFT against cold atom simulators. In a collaboration with the Esslinger group at ETH Zurich [Phys. Rev. Lett. 123, 193602 (2019)], we studied the excitation of electrons across the Mott gap in a periodically driven, strongly interacting Hubbard model. The illustration shows the production of double occupations for different pulse amplitudes K0. The left panel illustrates the experimental result, while the right hand side shows the DMFT result for the same setup. Up to the timescale where the comparison is meaningful (before the gray shaded region), the two results agree well, which shows that our nonequilibrium DMFT framework provides quantitatively accurate predictions for nonequilibrium states in strongly correlated systems.
On the conceptual side, the Modmat project has produced numerous insights into mechanisms which can stabilize interesting nonthermal states, including eta-pairing states and nonthermal excitonic or spin/orbital orders. We also demonstrated that chiral superconducting states can be induced by photo-doping Mott insulators on geometrically frustrated lattices. In connection with experiments, an important step forward has been the clarification of the insulating nature of the correlated insulator 1T-TaS2, and its response to photo-doping.
When new methods are developed, it is important to benchmark them against available results. However, for nonequilibrium states of strongly correlated lattice systems, few established methods exist. We therefore benchmarked nonequilibrium DMFT against cold atom simulators. In a collaboration with the Esslinger group at ETH Zurich [Phys. Rev. Lett. 123, 193602 (2019)], we studied the excitation of electrons across the Mott gap in a periodically driven, strongly interacting Hubbard model. The illustration shows the production of double occupations for different pulse amplitudes K0. The left panel illustrates the experimental result, while the right hand side shows the DMFT result for the same setup. Up to the timescale where the comparison is meaningful (before the gray shaded region), the two results agree well, which shows that our nonequilibrium DMFT framework provides quantitatively accurate predictions for nonequilibrium states in strongly correlated systems.