  We model a quantum dot-array (with one electron per dot) comprising of two
(or more than two) coupled dots by an extended Hubbard Hamiltonian to
investigate the role played by the inter-dot tunneling amplitude td, together
with intra-dot (U) and inter-dot(U1) coulomb repulsions, in the singlet /
triplet bound state formation and evolution of the system from the
Mott-insulator-like state to a correlated semi-metallic state via
charge-bond-order route. In the presence of magnetic field, td is complex due
to the appearance of Peierls phase factor. We introduce a short-ranged
inter-dot capacitive coupling U0, assumed to be non-zero for nearest-neighbor
dots only, for the bound state analysis. The study indicates that, while for
the tunable parameter d = (2td/U0) greater than unity only the possibility of
the triplet bound state formation exists, for d less than one both triplet and
singlet states are possible. The bound states are formed due to tunneling and
capacitive dot-bondings with coulomb interactions (U,U1) playing marginal role.
The interaction U, however, is found to play, together with complex td, an
important role in the evolution of the double quantum dot system from the
insulator-like state to that of a correlated semi-metallic state through
charge-bond-ordering route.
