Pseudofermion method for the exact description of fermionic environments: From single-molecule electronics to the Kondo resonance

We develop a discrete fermion approach for modeling the strong interaction of an arbitrary system interacting with continuum electronic reservoirs. The approach is based on a pseudofermion decomposition of the continuum bath correlation functions and is only limited by the accuracy of this decomposition. We show that to obtain this decomposition, one can allow for imaginary pseudofermion parameters, and strong damping in individual pseudofermions, without introducing unwanted approximations. For a noninteracting single-resonant level, we benchmark our approach against an analytical solution and an exact hierarchical-equations-of-motion approach. We also show that, for the interacting case, this simple method can capture the strongly correlated low-temperature physics of Kondo resonance, even in the difficult scaling limit, by employing matrix product state techniques.