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

Abstract

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 $|F=1,\text{ }{m}_{F}=1⟩$ 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.