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We investigate magnetism and quantum phase transitions in a one-dimensionalsystem of integrable spin-1 bosons with strongly repulsive density-densityinteraction and antiferromagnetic spin exchange interaction via thethermodynamic Bethe ansatz method. At zero temperature, the system exhibitsthree quantum phases: (i) a singlet phase of boson pairs when the externalmagnetic field $H$ is less than the lower critical field $H_{c1}$; (ii) aferromagnetic phase of atoms in the hyperfine state $|F=1, m_{F}=1>$ when theexternal magnetic field exceeds the upper critical field $H_{c2}$; and (iii) amixed phase of singlet pairs and unpaired atoms in the intermediate region$H_{c1}<H<H_{c2}$. At finite temperatures, the spin fluctuations affect thethermodynamics of the model through coupling the spin bound states to thedressed energy for the unpaired $m_{F}=1$ bosons. However, such spin dynamicsis suppressed by a sufficiently strong external field at low temperatures. Thusthe singlet pairs and unpaired bosons may form a two-component Luttinger liquidin the strong coupling regime.

Magnetism of one-dimensional strongly repulsive spin-1 bosons with antiferromagnetic spin exchange interaction