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

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