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An exhaustive ground-state analysis of extended two-dimensional (2D)correlated spin-electron model consisting of the Ising spins localized on nodallattice sites and mobile electrons delocalized over pairs of decorating sitesis performed within the framework of rigorous analytical calculations. Theinvestigated model, defined on an arbitrary 2D doubly decorated lattice, takesinto account the kinetic energy of mobile electrons, the nearest-neighbor Isingcoupling between the localized spins and mobile electrons, the further-neighborIsing coupling between the localized spins and the Zeeman energy. Theground-state phase diagrams are examined for a wide range of model parametersfor both ferromagnetic as well as antiferromagnetic interaction between thenodal Ising spins and non-zero value of external magnetic field. It is foundthat non-zero values of further-neighbor interaction leads to a formation ofnew quantum states as a consequence of competition between all consideredinteraction terms. Moreover, the new quantum states are accompanied withdifferent magnetic features and thus, several kinds of discontinuousfield-driven phase transitions are observed.

The influence of further-neighbor spin-spin interaction on a ground state of 2D coupled spin-electron model in a magnetic field