Ground-state Competition of Two-Component Bosons in Optical Lattice near a Feshbach Resonance

We investigate the ground state properties of an equal mixture of two species of bosons in its Mott-insulator phase at a filling factor two per site. We identify one type of spin triplet-singlet transition through the competition of ground state. When the on-site interaction is weak ($U<U_c$) the two particles prefer to stay in the lowest band and with weak tunnelling between neighboring sites the system is mapped into an effective spin-1 ferromagnetic exchange Hamiltonian. When the interaction is tuned by a Feshbach resonance to be large enough ($U>U_c$), higher band will be populated. Due to the orbital coupling term $S^+S^-$ in the Hamiltonian, the two atoms in different orbits on a site would form an on-site singlet. For a non-SU(2)-symmetric model, easy-axis or easy-plane ferromagnetic spin exchange models may be realized corresponding to phase separation or counter-flow superfluidity, respectively.