https://doi.org/10.1140/epjst/e2010-01219-x
Review
New theoretical approaches for correlated systems in nonequilibrium
1 Institute of Theoretical Physics, ETH Zürich, Wolfgang-Pauli-Str. 27, 8093 Zürich, Switzerland
2 Institute of Theoretical Physics, Universität zu Köln, Zülpicher Str. 77, 50937 Köln, Germany
3 Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Physics Department, Ludwig-Maximilians-Universität München, Theresienstr. 37, 80333 München, Germany
4 Theoretical Physics III, Center for Electronic Correlations and Magnetism, Institute of Physics, Universität Augsburg, 86135 Augsburg, Germany
5 Max Planck Institute of Quantum Optics, Hans-Kopfermann-Str. 1, 85748 Garching, Germany
We review recent developments in the theory of interacting quantum many-particle systems that are not in equilibrium. We focus mainly on the nonequilibrium generalizations of the flow equation approach and of dynamical mean-field theory (DMFT). In the nonequilibrium flow equation approach one first diagonalizes the Hamiltonian iteratively, performs the time evolution in this diagonal basis, and then transforms back to the original basis, thereby avoiding a direct perturbation expansion with errors that grow linearly in time. In nonequilibrium DMFT, on the other hand, the Hubbard model can be mapped onto a time-dependent self-consistent single-site problem. We discuss results from the flow equation approach for nonlinear transport in the Kondo model, and further applications of this method to the relaxation behavior in the ferromagnetic Kondo model and the Hubbard model after an interaction quench. For the interaction quench in the Hubbard model, we have also obtained numerical DMFT results using quantum Monte Carlo simulations. In agreement with the flow equation approach they show that for weak coupling the system relaxes to a “prethermalized” intermediate state instead of rapid thermalization. We discuss the description of nonthermal steady states with generalized Gibbs ensembles.
© EDP Sciences, Springer-Verlag, 2010
