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We study relaxation dynamics in a strongly-interacting two-site Fermi-Hubbardmodel that is induced by coupling each site to a local fermionic bath. Toderive the proper form of the Lindblad operators that enter an effectivedescription of the system-bath coupling in different temperature regimes, weemploy a diagrammatic real-time technique for the time evolution of the reduceddensity matrix. In spite of a local coupling to the baths, the found Lindbladoperators are non-local in space. We compare with the local approximation,where those non-local effects are neglected. Furthermore, we propose animprovement on the commonly-used secular approximation (rotating-waveapproximation), referred to as coherent approximation, which turns out superiorin all studied parameter regimes (and equivalent otherwise). We look at therelaxation dynamics for several important observables and compare the methodsfor early and late times in various temperature regimes.

Relaxation dynamics in a Hubbard dimer coupled to fermionic baths: phenomenological description and its microscopic foundation