Spectral properties of correlated quantum wires and carbon nanotubes within the Generalized Kadanoff-Baym Ansatz

TL;DR

This paper evaluates the effectiveness of the Generalized Kadanoff-Baym Ansatz (GKBA) in capturing spectral properties of correlated quantum wires and nanotubes, comparing it with full Kadanoff-Baym equations.

Contribution

It demonstrates that GKBA with Hartree-Fock propagators accurately reproduces spectral features of complex quantum systems, validating its use for such analyses.

Findings

GKBA captures main spectral features of the systems.

Comparison shows good agreement with full Kadanoff-Baym solutions.

Method applicable to quantum wires and nanotubes.

Abstract

We investigate the spectral properties of an open interacting system by solving the Generalized Kadanoff-Baym Ansatz (GKBA) master equation for the single-particle density matrix, namely the time-diagonal lesser Green's function. To benchmark its validity, we compare the solution obtained within the GKBA with the solution of the Dyson equation (equivalently the full Kadanoff-Baym equations). In both approaches, we treat the interaction within the self-consistent second-order Born approximation, whereas the GKBA still retains the retarded propagator calculated at the Hartree-Fock level. We consider the case of two leads connected through a central correlated region where particles can interact and exploit the stationary particle current at the boundary of the junction as a probe of the spectral features of the system. In this work, as an example, we take the central region to be a one-dimensional quantum wire and a two-dimensional carbon nanotube and show that the solution of the GKBA master equation well captures their spectral features. Our result demonstrates that, even when the propagator used is at the Hartree-Fock level, the GBKA solution retains the main spectral features of the self-energy used.