Time-Dependent and Steady-State Gutzwiller approach for nonequilibrium transport in nanostructures

TL;DR

This paper extends the time-dependent Gutzwiller variational approach to impurity problems, derives a steady-state theory, and applies it to quantum dot models, showing promising results and pathways for systematic improvements.

Contribution

The paper introduces a consistent steady-state extension of the time-dependent Gutzwiller approach for nonequilibrium transport in nanostructures, with initial applications to impurity models.

Findings

The method captures dissipation and reaches steady state after relaxation.

Comparison with quantum Monte Carlo validates the approach within certain limits.

The approach can be systematically improved by expanding the Gutzwiller projector region.

Abstract

We extend the time-dependent Gutzwiller variational approach, recently introduced by Schir\`o and Fabrizio, Phys. Rev. Lett. 105 076401 (2010), to impurity problems. Furthermore, we derive a consistent theory for the steady state, and show its equivalence with the previously introduced nonequilibrium steady-state extension of the Gutzwiller approach. The method is shown to be able to capture dissipation in the leads, so that a steady state is reached after a sufficiently long relaxation time. The time-dependent method is applied to the single orbital Anderson impurity model at half-filling, modeling a quantum dot coupled to two leads. In these first exploratory calculations the Gutzwiller projector is limited to act only on the impurity. The strengths and the limitations of this approximation are assessed via comparison with state of the art continuous time quantum Monte Carlo results. Finally, we discuss how the method can be systematically improved by extending the region of action of the Gutzwiller projector.