FWF - Nonequilibrium Master approach - Nonequilibrium correlated systems: auxiliary Master approach

In many materials, the active electrons can be safely considered as independent particles moving in the background of the other constituent particles. Theoretically, this means that they can be treated within an effective single-particle approach. Strongly correlated systems are materials for which this picture does not work. Besides making their theoretical description more challenging, this feature is often accompanied with a variety of remarkable electronic and magnetic properties. This class of systems includes a number of transition-metal oxides, such as high-Tc superconductors, spintronic materials, and heavy-fermion compounds. Strong correlation phenomena can be also artificially produced in ultracold atoms in optical lattices. In recent years there has been a rapid development of experimental techniques capable of microscopically controlling and of engineering the dynamics of many-body quantum mechanical states: from quantum optics, to solid state nanoscience, molecular electronics, spintronics, and ultrafast laser spectroscopy. This has boosted the interest in theoretically understanding correlated systems out of equilibrium. This project aims at developing, extending and applying a new theoretical scheme to deal with strongly correlated quantum-many-body systems out of equilibrium in their steady state. The numerical approach is based upon the so-called dynamical-mean-field theory (DMFT) within the nonequilibrium (Keldysh) Green's functions formalism. In particular, the method presents a new route towards the solution of the DMFT “bottleneck”, the steady-state correlated impurity problem, with controlled accuracy. The idea is based on embedding the impurity in a mixed environment consisting of discrete bath sites and a Markovian (i.e. memory-less) surroundings. The first part of the project consists in the development of several aspects of the technique, to be used in the second part. This section will aim at improving the accuracy of the method and implementing and testing more efficient techniques for the solution of the above-mentioned "mixed-environment" impurity problem. Further developments will focus on the long-range part of the Coulomb interaction, as well as at the treatment of the coupling of electrons to acoustic phonons in order to study heat transport. In the applicative part of the project, we plan to study nonequilibrium properties of artificial heterostructures of materials for which strong correlations play an important role, such as, e.g. layered transition metal oxides. We will focus on nonlinear transport, as well as on the study of possible nonequilibrium-driven phase transitions to magnetic or superconducting phases. We will also study the interplay of electron-electron and electron-phonon interaction out of equilibrium. In particular, we will focus on the relation between electron transport and heat dissipation in the presence of strong correlations, for simple toy models as well as for the correlated heterostructures discussed above.