  We consider a ring of fermionic quantum sites, modeled by the Fermi-Hubbard
Hamiltonian, in which electrons can move and interact strongly via the Coulomb
repulsion. The system is coupled to fermionic cold baths which by the exchange
of particles and energy induce relaxation in the system. We eliminate the baths
and describe the system effectively by the Lindblad master equations in various
versions valid for different coupling parameter regimes. The early relaxation
phase proceeds in a universal way, irrespective of the relative couplings and
approximations. The system settles down to its low-energy sector and is
consecutively well approximated by the Heisenberg model. In the late
relaxation, different Lindblad approaches push the system towards different
final states with opposite, extreme spin orders, from ferromagenetic to
antiferromagnetic. Due to spin frustration in the trimer (a three site ring),
degenerate ground states are formed by spin waves (magnons). The system
described by the global coherent version of the Lindblad operators relaxes
towards the final states carrying directed persistent spin currents. We
numerically confirm these predictions.
