FWF - Clustermethoden - Clustermethods for correlated systems out of equilibrium

The understanding of the nonequilibrium behavior of strongly correlated quantum many-body systems is a long standing challenge, both in theory as well as in experiments. The enormous progress and level of control achieved in various fields such as quantum optics, quantum simulation, heterostructures, nanotechnology and spintronics, renders nonequilibrium properties increasingly relevant. In many of the investigated systems, strong correlations play a crucial role to fully understand their physical properties. In this project, we plan to develop a new numerical approach that allows to calculate nonequilibrium steady state properties of strongly correlated quantum many-body systems. We have recently published preliminary test calculations of this method on the preprint archive. The approach is formulated in the framework of Keldysh Green's functions and is based on the ideas of the variational cluster approach (VCA), which has been successfully applied to a variety of strongly correlated many-body systems in equilibrium. This broad applicability also generalizes to the nonequilibrium method proposed here. In particular, the proposed approach can treat both fermions and bosons, is applicable in any spatial dimension, and can treat systems, where the strongly correlated region is spatially extended. Furthermore, the nonequilibrium method is neither perturbative in the many-body interaction nor in the field, that drives the system out of equilibrium. As in equilibrium VCA, one crucial aspect appears to be the variational procedure, consisting in a self-consistent adjustment of the equilibrium reference system to the nonequilibrium target state. A detailed analysis of the various options and of their performance will be one of the aspects dealt with in this project. The method shall be tested and applied to a number of physically interesting models. We expect our proposed method to provide valuable insight into the nonequilibrium physics of strongly correlated many-body systems, complementary to the ones obtained by approaches developed up to now. A sound understanding of fundamental nonequilibrium properties of quantum many-body systems might help to pave the way for the enhancement and invention of several high-tech applications, which might be rooted in the fields of material science or quantum information.