We study electron quantum transport through a strongly interacting Anderson quantum dot at finite bias voltage and magnetic field at zero temperature using the real-time renormalization group (RT-RG) in the framework of a kinetic (generalized master) equation for the reduced density operator. To this end, we further develop the general, finite-temperature real-time transport formalism by introducing field superoperators that obey fermionic statistics. This direct second quantization in Liouville Fock space strongly simplifies the construction of operators and superoperators that transform irreducibly under the Anderson-model symmetry transformations. The fermionic field superoperators naturally arise from the univalence (fermion-parity) superselection rule of quantum mechanics for the total system of quantum dot plus reservoirs. Expressed in these field superoperators, the causal structure of the perturbation theory for the effective time-evolution superoperator kernel becomes explicit. Using the constraints of the causal structure, we construct a parametrization of the exact effective time-evolution kernel for which we analytically find the eigenvectors and eigenvalues in terms of a minimal set of only 30 independent coefficients. The causal structure also implies the existence of a fermion-parity protected eigenvector of the exact Liouvillian, explaining a recently reported result on adiabatic driving [Contreras-Pulido et al., Phys. Rev. B 85, 075301 (2012)] and generalizing it to arbitrary order in the tunnel coupling . Furthermore, in the wide-band limit, the causal representation exponentially reduces the number of diagrams for the time-evolution kernel. The remaining diagrams can be identified simply by their topology and are manifestly independent of the energy cutoff term by term. By an exact reformulation of this series, we integrate out all infinite-temperature effects, obtaining an expansion targeting only the nontrivial, finite-temperature corrections, and the exactly conserved transport current follows directly from the time-evolution kernel. From this new series, the previously formulated RT-RG equations are obtained naturally. We perform a complete one-plus-two-loop RG analysis at finite voltage and magnetic field, while systematically accounting for the dependence of all renormalized quantities on both the quantum dot and reservoir frequencies. Using the second quantization in Liouville space and symmetry restrictions, we obtain analytical RT-RG equations, which can be solved numerically in an efficient way, and we extensively study the model parameter space, excluding the Kondo regime where the one-plus-two-loop approach is obviously invalid. The incorporated renormalization effects result in an enhancement of the inelastic cotunneling peak, even at a voltage ∼magnetic field ∼tunnel coupling . Moreover, we find a tunnel-induced nonlinearity of the stability diagrams (Coulomb diamonds) at finite voltage, both in the single-electron tunneling and inelastic cotunneling regime.

We study the transient heat current out of a confined electron system into a weakly coupled electrode in response to a voltage switch. We show that the decay of the Coulomb interaction energy for this repulsive system exhibits signatures of electron-electron attraction, and is governed by an interaction-independent rate. This can only be understood from a general duality that relates the non-unitary evolution of a quantum system to that of a dual model with inverted energies. Deriving from the fermion-parity superselection postulate, this duality applies to a large class of open systems.PACS numbers: 73.63.Kv, Energy decay due to heat currents is of key importance in the continued downscaling of electronic devices [1]. The quantum [2][3][4][5][6] and interaction effects [7][8][9] that arise on the nanoscale give rise to new possibilities [10][11][12][13] and motivate both fundamental [14] and application oriented [3, 4, 8, 13, 15] studies on quantum heatengines, possibly realized in, e.g., cold atoms, trapped ions, or quantum dots. The successful control and exploitation of heat in nanodevices requires both a fundamental understanding and the practical ability to detect and manipulate few-electron heat currents. Under stationary conditions, progress has been achieved using various approaches [16][17][18], including heat transfer through molecular-scale devices [19] with electrostatic gating [20]. However, any device is eventually adjusted by some external agent that provokes a time-dependent response. In the context of electronic heat currents, this raises a very basic question that, despite recent promising theoretical [21][22][23][24][25][26][27] and experimental [28][29][30] studies, has not been answered so far: how does a small electron system, typically governed by a strong level-quantization and Coulomb interaction, dissipate in time its stored energy into a coupled electronic bath?The essence of time-dependent transport in such systems is already captured by the simple model sketched in Figs. 1(a,b). Here, an instant energy shift of a single electronic orbital in a quantum dot leads to a timedependent charge current I N (t) [31,32] and heat current I Q (t) into a tunnel-coupled electrode. In the weak coupling regime, expressions for these currents can be calculated straightforwardly, and in the case of the transient charge current I N (t) also allow for an intuitive physical understanding [33]. This is, however, not the case for the heat current I Q (t) = a c e −γct +a p e −γpt . Compared to the charge current I N (t) ∝ e −γct , the heat current contains a second decay mode. The mere presence of this mode can be expected: it originates from the dissipation of the Coulomb energy. However, what is quite remarkable is that its rate γ p turns out to be completely independent of the interaction strength U [34-37] -despite entering the heat current only as a consequence of the interaction. Even more surprisingly, as indicated by the blue dashed line in Fig. 1(e 2 dealing with a system governed by repulsive i...

We extend the recently developed causal superfermion approach to the real-time diagrammatic transport theory to time-dependent decay problems. Its usefulness is illustrated for the Anderson model of a quantum dot with tunneling rates depending on spin due to ferromagnetic electrodes and / or spin polarization of the tunnel junction. This approach naturally leads to an exact result for one of the time-dependent decay modes for any value of the Coulomb interaction compatible with the wideband limit. We generalize these results to multilevel Anderson models and indicate constraints they impose on renormalization-group schemes in order to recover the exact noninteracting limit.(i) We first set up a second quantization scheme in the space of density operators constructing "causal" field superoperators using the fundamental physical principles of causality / probability conservation and fermion-parity superselection (univalence). The time-dependent perturbation series for the time-evolution is renormalized by explicitly performing the wideband limit on the superoperator level. As a result, the occurrence of destruction and creation superoperators are shown to be tightly linked to the physical short-and long-time reservoir correlations, respectively. This effective theory takes as a reference a damped local system, which may also provide an interesting starting point for numerical calculations of memory kernels in real time.(ii) A remarkable feature of this approach is the natural appearance of a fermion-parity protected decay mode which can be measured using a setup proposed earlier [Phys. Rev. B 85, 075301 (2012)]. This mode can be calculated exactly in the fully Markovian, infinite-temperature limit by leading order perturbation theory, but surprisingly persists unaltered for finite temperature, for any interaction and tunneling spin polarization.(iii) Finally, we show how a Liouville-space analog of the Pauli principle directly leads to an exact expression in the noninteracting limit for the time evolution, extending previous works by starting from an arbitrary initial mixed state including spin-and pairing coherences and two-particle correlations stored on the quantum dot. This exact result is obtained already in finite-order renormalized perturbation theory, which surprisingly is not quadratic but quartic in the field superoperators, despite the absence of Coulomb interaction. The latter fact we relate to the time-evolution of the two-particle component of the mixed state, which is just the fermion-parity operator, a cornerstone of the formalism. We illustrate how the super-Pauli principle also simplifies problems with nonzero Coulomb interaction.