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arXiv:1506.07360 · New Journal of Physics

Non-equilibrium transport through a model quantum dot: Hartree–Fock approximation and beyond

Christian Schiegg, Michael Dzierzawa, Ulrich Eckern

Published Aug 28, 2015• 3 citations
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Abstract

The finite-temperature transport properties of the spinless interacting fermion model coupled to non-interacting leads are investigated. Employing the unrestricted time-dependent Hartree–Fock (HF) approximation, the transmission probability and the nonlinear I – V characteristics are calculated, and compared with available analytical results and with numerical data obtained from a Hubbard–Stratonovich decoupling of the interaction. In the weak interaction regime, the HF approximation reproduces the gross features of the exact I – V characteristics but fails to account for subtle properties like the particular power law for the reflected current in the interacting resonant level model.

DOI
10.1088/1367-2630/17/8/083060

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The finite-temperature transport properties of the spinless interacting fermion model coupled to non-interacting leads are investigated. Employing the unrestricted time-dependent Hartree–Fock (HF) approximation, the transmission probability and the nonlinear I – V characteristics are calculated, and compared with available analytical results and with numerical data obtained from a Hubbard–Stratonovich decoupling of the interaction. In the weak interaction regime, the HF approximation reproduces the gross features of the exact I – V characteristics but fails to account for subtle properties like the particular power law for the reflected current in the interacting resonant level model.
We study transport properties of quantum impurity systems using the functional renormalization group. The latter is an RG-based diagrammatic tool to treat Coulomb interactions in a fast and flexible way. Prior applications, which employed a simple first-order (Hartree-Fock-like) scheme to truncate the FRG flow equations within the Matsubara formalism, succeeded in accurately describing linear transport of various quantum dot geometries at zero temperature T=0. In a nutshell, advance in this Thesis is three-fold. First, we introduce a frequency-dependent second-order approximation in order to eventually compute finite-energy properties such as the conductance at T>0 (mainly focusing on the single impurity Anderson model). Second, a generalisation of the Hartree-Fock-like approach to Keldysh space allows for addressing the non-equilibrium steady-state dynamics of the interacting resonant level model. Third, we investigate the physics of a quantum dot Josephson junction as well as the charging of a single narrow level using the first-order scheme.
The spin transport in a strongly interacting spin-pump nanodevice is studied using the time-dependent variational-matrix-product-state approach. The precession magnetic field generates a dissipationless spin current through the quantum dot. We compute the real-time spin current away from the equilibrium condition. Both transient and stationary states are reached in the simulation. The essentially exact results are compared with those from the Hartree-Fock approximation (HFA). It is found that correlation effect on the physical quantities at quasisteady state are captured well by the HFA for small interaction strength. However the HFA misses many features in the real-time dynamics. Results reported here may shed light on the understanding of the ultrafast processes as well as the interplay of the nonequilibrium and strongly correlated effect in the transport properties.
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We analyze nonequilibrium electronic transport properties of a typical interacting three-site quantum wire model within Hartree-Fock approximation making use of Keldysh formalism. Some rigorous formulas are provided for direct calculations when Coulomb repulsion is present. According to numerical calculations using above formulas, we investigate the conductance, transport currents, and on site electronic charges of the wire on some special occasions in the interacting case, and also compare them with the results in the noninteracting case.
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We investigate equilibrium and steady-state nonequilibrium transport properties of a spinless resonant level locally coupled to two conduction bands of width $\ensuremath{\sim}\ensuremath{\Gamma}$ via a Coulomb interaction UUU and a hybridization ${t}^{\ensuremath{'}}$. In order to study the effects of finite bias voltages beyond linear response, a generalization of the functional renormalization group to Keldysh frequency space is employed. Being mostly unexplored in the context of quantum impurity systems out of equilibrium, we benchmark this method against recently published time-dependent density matrix renormalization group data. We thoroughly investigate the scaling limit $\ensuremath{\Gamma}\ensuremath{\rightarrow}\ensuremath{\infty}$ characterized by the appearance of power laws. Most importantly, at the particle-hole symmetric point the steady-state current decays like $J\ensuremath{\sim}{V}^{\ensuremath{-}{\ensuremath{\alpha}}_{J}}$ as a function of the bias voltage $V⪢{t}^{\ensuremath{'}}$, with an exponent ${\ensuremath{\alpha}}_{J}(U)$ that we calculate to leading order in the Coulomb interaction strength. In contrast, we do not observe a pure power-law (but more complex) current-voltage-relation if the energy ϵϵϵ of the resonant level is pinned close to either one of the chemical potentials $\ifmmode\pm\else\textpm\fi{}V/2$.