  An exhaustive ground-state analysis of extended two-dimensional (2D)
correlated spin-electron model consisting of the Ising spins localized on nodal
lattice sites and mobile electrons delocalized over pairs of decorating sites
is performed within the framework of rigorous analytical calculations. The
investigated model, defined on an arbitrary 2D doubly decorated lattice, takes
into account the kinetic energy of mobile electrons, the nearest-neighbor Ising
coupling between the localized spins and mobile electrons, the further-neighbor
Ising coupling between the localized spins and the Zeeman energy. The
ground-state phase diagrams are examined for a wide range of model parameters
for both ferromagnetic as well as antiferromagnetic interaction between the
nodal Ising spins and non-zero value of external magnetic field. It is found
that non-zero values of further-neighbor interaction leads to a formation of
new quantum states as a consequence of competition between all considered
interaction terms. Moreover, the new quantum states are accompanied with
different magnetic features and thus, several kinds of discontinuous
field-driven phase transitions are observed.
