Abstract
Finite lattice systems represent the (computationally) simplest class of inhomogeneous quantum systems. This fact explains why a relatively large number of NEGF studies are available including the Anderson (impurity) model, the Hubbard model and even sophisticated quantum transport models involving leads.
The present chapter begins with a chronological literature overview listing the most important publications and also recent advances in the field. Furthermore, to give a tutorial example, a minimal Fermi-Hubbard model is explored at various interaction strengths and for excitations in the linear and non-linear response regimes. The results are based on the second Born approximation and the generalized Kadanoff-Baym ansatz (GKBA). In the course of this, the GKBA is proven to overcome problems observed in two-time calculations for finite systems, such as artificial steady states.
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- 1.
- 2.
While LDA means “local-density approximation”, the parameter U indicates a purely local Hubbard-type interaction, cf. Sect. 5.2.
- 3.
The hopping amplitude is related to the overlap between the one-particle orbitals on different lattice sites.
- 4.
Although the exact finite lattice system has a finite number of poles.
- 5.
There is one up- and one down-spin electron in the system (N=N ↑+N ↓=2).
- 6.
We emphasize that energy and particle number conservation is fulfilled at all times.
- 7.
The GKBA data are provided by S. Hermanns (University Kiel) [178].
- 8.
A double excitation is a correlation-induced process where two electrons are excited simultaneously.
- 9.
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S. Hermanns, K. Balzer, M. Bonitz, in preparation (2012)
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Balzer, K., Bonitz, M. (2013). Lattice Systems. In: Nonequilibrium Green's Functions Approach to Inhomogeneous Systems. Lecture Notes in Physics, vol 867. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35082-5_5
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