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Exact eigenstates of the parallel coupled double quantum dots attached to thenon-interacting leads taken in zero-bandwidth limit are analytically obtainedin each particle and spin sector. The ground state of the half-filled system isidentified from a four dimensional subspace of the twenty dimensional Hilbertspace for different values of tunable parameters of the system viz. the energylevels of the quantum dots, the interdot tunneling matrix-element, the ondotand interdot Coulomb interactions and quantities like spin-spin correlationbetween the dots, occupancies of the dots are calculated. In the parameterspace of the interdot tunneling matrix-element and ondot Coulomb interaction,the dots exhibit both ferromagnetic and antiferromagnetic correlation. There isa critical dependency of the interdot tunneling matrix-element on the ondotCoulomb interaction which leads to transition from the ferromagneticcorrelation to the antiferromagnetic correlation as the interdot tunnelingmatrix-element is increased. The ferromagnetic and antiferromagneticcorrelations also exist in the absence of interdot tunneling matrix-elementthrough indirect exchange via the leads. The interdot Coulomb interaction isfound to affect this dependency considerably.

Exact diagonalization study of double quantum dots in parallel geometry in zero-bandwidth limit