Free energy in a spin transport among particles in a Fermi-Hubbard optical lattice

The Fermi-Hubbard model investigates the dynamics of fermions confined in a one-dimensional (1D) optical lattice. In turn, the lattice is confined to a heat bath consisting of a fermionic quantum gas. Here, we use the path integral method to investigate the effects of the coupling at zero temperature and determine the five processes among bath particles which facilitate spin transport among optical lattice particles. Furthermore, we compute for the free energy per lattice site during such process.