New theoretical approaches for correlated systems in nonequilibrium

TL;DR

This paper reviews recent theoretical advances in modeling nonequilibrium correlated quantum systems, focusing on flow equation methods and dynamical mean-field theory, highlighting their applications to transport, relaxation, and steady states.

Contribution

It introduces and compares the nonequilibrium flow equation approach and dynamical mean-field theory for correlated systems, emphasizing new computational techniques and their applications.

Findings

Flow equation approach effectively models nonlinear transport in the Kondo model.

Numerical DMFT results show weakly coupled systems relax to prethermalized states.

Agreement between flow equation and DMFT results on relaxation dynamics.

Abstract

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.