  The spin-1/2 Heisenberg orthogonal-dimer chain is considered within the
perturbative strong-coupling approach, which is developed from the exactly
solved spin-1/2 Ising-Heisenberg orthogonal-dimer chain with the Heisenberg
intradimer and the Ising interdimer couplings. Although the spin-1/2
Ising-Heisenberg orthogonal-dimer chain exhibits just intermediate plateaux at
zero, one-quarter and one-half of the saturation magnetization, the
perturbative treatment up to second order stemming from this exactly solvable
model additionally corroborates the fractional one-third plateau as well as the
gapless Luttinger spin-liquid phase. It is evidenced that the approximate
results obtained from the strong-coupling approach are in an excellent
agreement with the state-of-the-art numerical data obtained for the spin-1/2
Heisenberg orthogonal-dimer chain within the exact diagonalization and
density-matrix renormalization group method. The nature of individual quantum
ground states is comprehensively studied within the developed perturbation
theory.
