Skip to main content

Real-time dynamics of correlated many-body systems

Final Report Summary - DYNCORSYS (Real-time dynamics of correlated many-body systems)

The goal of the DYNCORSYS project was to develop the nonequilibrium extension of dynamical mean field theory into a powerful and versatile tool for the simulation of nonequilibrium phenomena in correlated lattice systems. Dynamical mean field theory is an approximate scheme which is widely used in the study of equilibrium properties of strongly correlated lattice problems, with applications ranging from crystalline solids to cold atoms trapped in optical lattices and quantum field theories. The formalism was extended to nonequilibrium systems about ten years ago, in order to treat the realtime dynamics of such systems after an external perturbation (typically a strong laser pulse in the case of solids, or a rapid change in the lattice potential in the case of cold atoms). By the time the DYNCORSYS project started in 2012, a number of important “proof of principle” calculations had been performed and it became clear that the formalism allows to simulate the dynamics of the most basic fermionic lattice models on experimentally relevant timescales.

Building on these pioneering studies, the DYNCORSYS effort extended the range of applicability of the nonequilibrium dynamical mean field approach in several important directions. In close collaboration with leading researchers in Germany and Japan, we have implemented the first nonequilibrium dynamical mean field simulations of symmetry-broken phases, bosonic lattice models, electron-phonon problems, and multi-orbital systems. We also extended the formalism to cluster embedding schemes (to treat nonlocal correlations), to inhomogeneous systems, and, within a so-called extended dynamical mean field framework, to models with long-ranged and dynamically screened interactions. While these are in principle direct generalizations of established equilibrium formalisms, the nonequilibrium implementations pose significant technical challenges and required the development and implementation of new algorithms for the solution of both fermionic and bosonic self-consistency equations in the complex time-plane. By the end of the DYNCORSYS project, essentially all existing flavors and variants of the dynamical mean field formalism had been extended to a relevant nonequilibrium set-up and systematically tested. The results of this effort, published in about 40 scientific articles, provide a fairly complete picture of the potential of this nonequilibrium simulation approach and the limitations of the presently available exact and approximate schemes for solving the dynamical mean field equations. The state of the field has been presented in detail in a Reviews of Modern Physics article, in which we not only discussed the technical details of the implementations, and recent applications, but also provided sample programs which should help other researchers to start their own investigations in this field.

On the applications side, the DYNCORSYS project produced important new insights into transient trapping phenomena and the relaxation dynamics of symmetry broken (magnetically ordered or superconducting) states, the effect of electron-spin and electron-lattice interactions on the cooling and life-time of photo-doped carriers, and into non-linear transport phenomena in the strong-field regime. The extended dynamical mean field approach and its combination with the GW method allowed to simulate the real-time dynamics of screening and provides the basis for the implementation of material-specific "ab-initio” simulations. Within a timeframe of five years, nonequilibrium dynamical mean field theory has thus advanced from the "proof of principles” stage into a sophisticated and versatile simulation tool which enables productive collaborations between theorist and experimentalists interested in the nonequilibrium dynamics of correlated lattice systems.