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We systematically study the effects of higher-order interactions on the S =3/2, 1 orthogonal dimer chains using exact diagonalization and density matrixrenormalization group. Due to frustration and higher spin, there are richquantum phases, including three Haldane phases, two gapless phases and severalmagnetically ordered phases. To characterize these phases and their phasetransitions, we study various physical quantities such as energy gap, energylevel crossing, fidelity susceptibility, spin correlation, entanglementspectrum and central charge. According to our calculations, the biquadraticterm can enhance the Haldane phase regions. In particular, we numericallyidentify that a Haldane phase in S = 3/2 case is adiabatically connected to theexact AKLT point when adding bicubic term. Our study on the orthogonal dimermodel, which is a 1D version of Shastry-Sutherland model, provides insightsinto understanding the possible S = 3/2, 1 Haldane phases in quasi-1D and 2Dfrustrated magnetic materials.

Haldane phases and phase diagrams of the S = 3/2, 1 bilinear-biquadratic Heisenberg model on the orthogonal dimer chain