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 Hc1; (ii) a ferromagnetic phase of atoms in the hyperfine state | F=1, mF =1 □ when the external magnetic field exceeds the upper critical field Hc2; and (iii) a mixed phase of singlet pairs and unpaired atoms in the intermediate region Hc1 <H< Hc2. 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 mF =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