Extended Hubbard model describing small multidot arrays in bilayer graphene

We set up and parametrize a Hubbard model for interacting quantum dots in bilayer graphene and study double dots as the smallest multidot system. We demonstrate the tunability of the spin and valley multiplets, Hubbard parameters, and effective exchange interaction by electrostatic gate potentials and the magnetic field. Considering both the long- and short-range Coulomb interactions, we map out the various spin and valley multiplets and calculate their energy gaps for different dot sizes and interdot separations. For half-filling and large valley splittings, we derive and parametrize an effective Heisenberg model for the quantum dot spins.