From integrability to conductance, impurity systems

We use the non-equilibrium Green's function formalism along with a self-consistent Hartree-Fock approximation to numerically study the effects of a single impurity and interactions between the electrons (with and without spin) on the conductance of a quantum wire. We study how the conductance varies with the wire length, the temperature, and the strength of the impurity and interactions. The dependence of the conductance on the wire length and temperature is found to be in ro...

The influence of electron--electron interaction on two terminal DC conductance of one--dimensional quantum wires is studied. A cancelation between the effect of the electron--electron interaction on the current and on the external electric field is the reason for the universal value, $e^2/2\pi\hbar $ per mode, of the DC conductance of a clean wire. The effect of the renormalization of the electric field on the DC conductance in the presence of an interplay between the electro...

A few exactly solvable interacting quantum many-body problems with impurities were previously reported to exhibit unusual features such as non-localization and absence of backscattering. In this work we consider the use of these integrable impurities as boundary conditions in the framework of linear transport problems. We first show that such impurities enhance the density of states at the Fermi surface, thus increasing the effective system size. The study of the real time-dy...

In this short paper we first give a very simple derivation of the Landauer formula for a 2-point conductance of QJ $G^{2P}$, based on the uncertainty principle. The aim of this is to introduce this central equation of quantum transport to a general audience. Next we analyse the dynamics of setting up a steady-state current in a simple many-electron system and use these observations to present physical basis and formal result for the 4-point conductance $G^{4P}$, rigorously re...

Understanding DC electrical conductivity is crucial for the study of materials. Macroscopic DC conductivity can be calculated from first principles using the Kubo-Greenwood equation. The procedure involves finding the thermodynamic limit of the current response to an electric field that is slowly switched on, and then taking the limit of the switching rate to zero. We introduce a nonlinear extrapolation procedure executed in systems with periodic boundary conditions, which pr...

We derive an exact expression for the Kubo conductunce in the Quantum Hall device with the point-like intra-edge backscattering. This involves the calculation of current-current correlator exactly, which we perform using form-factor method. In brief, the full set of intermediate states is inserted in the correlator, and for each term the closed mathematical expression is obtained. It is shown that by making a special choice of intermediate states in accordance with the hidden...

In computing electric conductivity based on the Kubo formula, the vertex corrections describe such effects as anisotropic scattering and quantum interference and are important to quantum transport properties. These vertex corrections are obtained by solving Bethe-Salpeter equations, which can become numerically intractable when a large number of k-points and multiple bands are involved. We introduce a non-iterative approach to the vertex correction based on rank factorization...

We develop in this letter an analytical approach using form- factors to compute time dependent correlations in integrable quantum impurity problems. As an example, we obtain for the first time the frequency dependent conductivity $G(\omega)$ for the tunneling between the edges in the $\nu=1/3$ fractional quantum Hall effect, and the spectrum $S(w)$ of the spin-spin correlation in the anisotropic Kondo model and equivalently in the double well system of dissipative quantum mec...

In this work we exploit the integrability of the two-lead Anderson model to compute transport properties of a quantum dot, in and out of equilibrium. Our method combines the properties of integrable scattering together with a Landauer-Buttiker formalism. Although we use integrability, the nature of the problem is such that our results are not generically exact, but must only be considered as excellent approximations which nonetheless are valid all the way through crossover re...

Formal but exact DC conductivity formulae for anisotropic Fermi liquids are reviewed. One is the Maebashi-Fukuyama formula based on the Fermi-surface harmonics. The other is the Taylor formula based on the scattering eigenfunction. In comparison to these two formulae the current-vertex-correction in the fluctuation-exchange approximation is shown to be a bad vision caused by an inconsistent approximation.