Fermionic versus spin baths in noninteracting transport models

We investigate how fermionic anticommutation shapes transport in a noninteracting resonant-level model where a single central site is coupled to an environment. To this end, we compare a fermionic reservoir with a bath of spin-½ modes using exact diagonalization and a perturbative expansion of the master equation to identify the differences. Notably, we find different reduced dynamics for the spin and fermionic baths even though both models restrict each local mode to at most one excitation; unlike the fermionic bath, however, the spin bath consists of commuting two-level modes and therefore lacks the global exchange antisymmetry of true fermions. These differences originate from higher-order terms in the system-bath coupling, where fermionic anticommutation introduces exchange signs in higher-order correlations. In contrast, all second-order contributions, set solely by two-point correlators, coincide. Deviations are largest for small to intermediate bath sizes, fading in the effectively Markovian regime where higher-order corrections are negligible. These results identify when spin baths can be a substitute for fermionic reservoirs and vice versa.