The exact ground state and the origin of the spin gap in the distorted mixed spin (1, 1/2) diamond chain

By using the method of exact diagonalization, we investigated the properties of the distorted mixed spin (1, 1/2) diamond chain with antiferromagnetic interactions along the rung and leg. The ground states of this model contain the sawtooth chain state and the rung dimer plus Haldane state. The research on the origin of the spin gap of the model discloses that there are three different types of spin excitations at different parameter regimes due to the competition among the interactions J1, J2 and J3.