  We systematically study the effects of higher-order interactions on the S =
3/2, 1 orthogonal dimer chains using exact diagonalization and density matrix
renormalization group. Due to frustration and higher spin, there are rich
quantum phases, including three Haldane phases, two gapless phases and several
magnetically ordered phases. To characterize these phases and their phase
transitions, we study various physical quantities such as energy gap, energy
level crossing, fidelity susceptibility, spin correlation, entanglement
spectrum and central charge. According to our calculations, the biquadratic
term can enhance the Haldane phase regions. In particular, we numerically
identify that a Haldane phase in S = 3/2 case is adiabatically connected to the
exact AKLT point when adding bicubic term. Our study on the orthogonal dimer
model, which is a 1D version of Shastry-Sutherland model, provides insights
into understanding the possible S = 3/2, 1 Haldane phases in quasi-1D and 2D
frustrated magnetic materials.
