The low-temperature properties of the spin-one Heisenberg antiferromagnetic chain with the single-ion anisotropy

► Low-temperature properties are obtained within the self-consistent method. ► The single-ion anisotropy suppresses quantum and thermal spin fluctuations. ► The exponents of low-temperature power-law increasing are dependent on the anisotropy. ► Our results agree with the quantum Monte Carlo, exact results and experimental data.