Time-dependent quantum transport: Causal superfermions, exact fermion-parity protected decay modes, and Pauli exclusion principle for mixed quantum states

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.