Nonequilibrium steady state for strongly-correlated many-body systems: variational cluster approach

TL;DR

This paper introduces a variational cluster approach within the Keldysh Green's function formalism to compute nonequilibrium steady states in strongly correlated quantum systems, enabling analysis of nonlinear responses and strong perturbations.

Contribution

It presents a novel, non-perturbative numerical method that combines variational cluster techniques with nonequilibrium Green's functions for strongly correlated systems.

Findings

Successfully applied to nonlinear transport in a Hubbard model quantum wire.

Bridges to cluster dynamical mean-field theory with increasing bath size.

Allows study of extended correlated regions under strong perturbations.

Abstract

A numerical approach is presented that allows to compute nonequilibrium steady state properties of strongly correlated quantum many-body systems. The method is imbedded in the Keldysh Green's function formalism and is based upon the idea of the variational cluster approach as far as the treatment of strong correlations is concerned. It appears that the variational aspect is crucial as it allows for a suitable optimization of a "reference" system to the nonequilibrium target state. The approach is neither perturbative in the many-body interaction nor in the field, that drives the system out of equilibrium, and it allows to study strong perturbations and nonlinear responses of systems in which also the correlated region is spatially extended. We apply the presented approach to non-linear transport across a strongly correlated quantum wire described by the fermionic Hubbard model. We illustrate how the method bridges to cluster dynamical mean-field theory upon coupling two baths containing and increasing number of uncorrelated sites.