Lattice Systems
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 soph
- PDF / 463,807 Bytes
- 8 Pages / 439.37 x 666.142 pts Page_size
- 30 Downloads / 176 Views
Lattice Systems
This chapter aims at giving a brief overview on the current status of Kadanoff-Baym approaches to lattice systems. To this end, we address the most relevant literature1 and, as a basic example, show NEGF results for a Hubbard-type dimer. As “lattice” systems, we generally denote quantum many-body systems where the particle motion is restricted to a finite or infinite set of localized sites in coordinate space. Prominent examples can be found in condensed matter systems and include, for example, the electron dynamics between the 3d (and/or 4f) orbitals in transition metal oxides—for respective LDA + U calculations2 see, e.g., Ref. [163]. However, the “lattice” sites need not necessarily be arranged in form of a well defined grid (i.e., on a real lattice described by a specific unit cell). Instead, also other nanoscale systems can directly be described by lattice-type Hamiltonians. Among these systems are, e.g., molecular junctions, small carbon nanotubes and wires, or atomic size point contacts. Theoretically as well as computationally, lattice systems can usually be described by a small set of parameters. This is due to the fact that the interaction between the charge carriers is typically short-ranged such that one can confine oneself to a purely local and (or) nearest-neighbor interaction. Furthermore, a specific hopping amplitude3 (resembling the kinetic energy) is often sufficient to describe the movement of the particles from one lattice site to another.
1 We mainly focus on papers, that apply specific many-body approximations to the KBEs and, for example, do not cover dynamical mean-field theory-based works. For an overview in this direction, see Refs. [42, 164] and references therein. 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.
K. Balzer, M. Bonitz, Nonequilibrium Green’s Functions Approach to Inhomogeneous Systems, Lecture Notes in Physics 867, DOI 10.1007/978-3-642-35082-5_5, © Springer-Verlag Berlin Heidelberg 2013
75
76
5 Lattice Systems
5.1 Overview The application of the Keldysh-Kadanoff-Baym formalism to the description of lattice systems in nonequilibrium to date mainly concerns the zero-temperature limit and small systems with a low number of single-particle states. To give a chronological overview, we first mention Ref. [165], where the Kondo effect and the zero-temperature transport properties of the Anderson impurity model have been studied on the level of the GW approximation by Thygesen and Rubio. Thereafter, the current-voltage (I V ) characteristics of a generic two-level system coupled to wide-band leads has been investigated in detail in Ref. [166]. Here, beyond the HF level, the inclusion of correlations in the 2B and GW approximation has led to an essential shift of the conductance peaks and an additional asymmetry in the peak profiles. As the responsible mechanism one
Data Loading...
