Electronic correlations in parallel-coupled double quantum dot system: An exact analytical approach

Exact eigenstates of the parallel coupled double quantum dots attached to the non-interacting leads taken in the zero-bandwidth limit (effectively quadruple quantum dots) are analytically obtained in each particle and spin subspace. The ground state of the half-filled system is determined within a four-dimensional subspace of the twenty-dimensional Hilbert space. The effects of tunable parameters, such as quantum dot energy levels, interdot tunneling, ondot and interdot Coulomb interactions, on spin-spin correlation and dot occupancies are analyzed. In the parameter space defined by interdot tunneling and ondot Coulomb interaction, the tunnel-coupled dots exhibit both ferromagnetic and antiferromagnetic correlations, suggesting suitability for singlet-triplet qubits in quantum computing. A critical dependency of interdot tunneling on ondot Coulomb interaction leads to a transition from ferromagnetic to antiferromagnetic correlation as interdot tunneling increases. These correlations persist even without interdot tunneling via indirect exchange through the leads, with the interdot Coulomb interaction significantly influencing this dependency.