On the basis of the method of iterative summation of path integrals (ISPI), we develop a numerically exact transfer-matrix method to describe the nonequilibrium properties of interacting quantum-dot systems. For this, we map the ISPI scheme to a transfer-matrix approach, which is more accessible to physical interpretation, allows for a more transparent formulation of the theory, and substantially improves the efficiency. In particular, the stationary limit is directly implemented, without the need of extrapolation. The resulting new method, referred to as "transfer-matrix summation of path integrals" (TraSPI), is then applied to resonant electronic transport through a single-level quantum dot.

Resonant tunneling of electrons between two ferromagnets and a quantum dot in the presence of an externally applied magnetic field reveals a strong gate dependence in the linear and nonlinear bias regime. This gate dependence originates from the interplay between Coulomb interactions and spin-dependent hybridization between the quantum dot and the leads. To take into account Coulomb interaction strengths of the same order of magnitude as the external magnetic field and the hybridization strength we adopt the numerically exact iterative summation of path integrals.

We report on the importance of resonant-tunneling processes on quantum transport through interacting quantum-dot spin valves. To include Coulomb interaction in the calculation of the tunneling magnetoresistance (TMR), we reformulate and generalize the recently developed, numerically exact method of iterative summation of path integrals (ISPI) to account for spin-dependent tunneling. The ISPI scheme allows us to investigate weak to intermediate Coulomb interaction in a wide range of gate and bias voltage and down to temperatures at which a perturbative treatment of tunneling severely fails.