Transport coefficients of the Anderson model via the numerical renormalization group

Abstract

The transport coefficients of the Anderson model are calculated by extending Wilson's numerical renormalization group method to finite temperature Green's functions. Accurate results for the frequency and temperature dependence of the single-particle spectral densities and transport time τ (ω, T ) are obtained and used to extract the temperature dependence of the transport coefficients in the strong correlation limit of the Anderson model. Results are obtained for values of the local level position ranging from the Kondo regime to the mixed valent and empty orbital regimes. The low temperature anomalies in the resistivity, ρ(T ), thermopower, S(T ), thermal conductivity κ(T ) and Hall coefficient, R H (T ), are discussed in terms of the behaviour of the spectral densities. All quantities exhibit the expected Fermi liquid behaviour at low temperature, ρ(T ). Analytic results based on Fermi liquid theory are derived here for the first time for β and the numerical results are shown to be consistent with this coefficient. The range of temperatures over which universal behaviour extends is also discussed. Scattering of conduction electrons in higher, l > 0, angular momentum channels is also considered and an expression is derived for the corresponding transport time and used to discuss the influence of the interference terms between the resonant l = 0 and non-resonant l = 1 channels on the transport properties.The presence of non-resonant scattering is shown to be particularly impor-tant for the thermopower at half-filling, where the sign of the thermopower can depend sensitively on the non-resonant phase shift. Finally the relation of the results to experiment is discussed.Address after 15th October 1993:

ConservingGWscheme for nonequilibrium quantum transport in molecular contacts

“…29,34 Another example is the Kondo effect which results from correlations between a localized spin on the molecule and delocalized electrons in the electrodes. 35,36 Third, as we will show here, the coupling to ͑noninteracting͒ electrodes enhances the screening on the molecule leading to characteristic reduction of the HOMO-LUMO gap as function of the electrode-molecule coupling strength.…”

“…For large U / ⌫, it is known 36,57 that the spectral function, in addition to the Kondo peak, should develop peaks at the atomic levels c and c + U. We find that the self-consistent 2B and GW approximations always fail to capture these sidebands and instead distribute the spectral weight as a broad slowly decaying tail.…”

“…36,57 Out of equilibrium, the low-temperature properties of the Anderson model have been much less studied. The earliest work addressed the problem by applying second-order perturbation theory in the interaction strength U.…”

Entanglement switching via the Kondo effect in triple quantum dots

“…One such method is the numerical renormalization-group (NRG) [42,43,[46][47][48]. It consists of a logarithmic discretization of the continuum of states of the conduction-band electrons, followed by a mapping to a one-dimensional chain Hamiltonian with exponentially decreasing hopping constants.…”

Single-molecule transport in three-terminal devices

“…The conduction mechanism for the Kondo effect involves spin-flip events such as the one illustrated in figure 3.4. We refer to other papers [40][41][42][43][44][45] for a more detailed theoretical discussion. Here, we concentrate on its main transport characteristics, which are summarized in figures 3.5 and 3.6.…”