We apply the Hubbard model, non-equilibrium Green's function (NEGF) theory,
exact diagonalization (ED) and the hierarchical equations of motion (HEOM)
method to investigate abundant magnetic phase transitions in the 1D interacting
quantum dots arrays (QDA) sandwiched by non-interaction leads. The spin
polarization phase transitions are firstly studied with a mean-field
approximation. The many-body calculation of the ED method is then used to
verify such transitions. We find with the weak device-leading couplings, the
anti-ferromagnetic (AF) state only exists in the uniform odd-numbered QDA or
the staggered-hopping QDA systems. With increasing the coupling strength or the
bias potentials, there exists the magnetism-to non-magnetism phase transition.
With the spin-resolved HEOM method we also investigate the detailed dynamic
phase transition process of these lead-QDA-lead systems.Comment: 17 pages, 6 figure