Villain transformation for XXZ anisotropic ferrimagnetic spin chain.

We investigate the spin excitation spectrum and the thermodynamic properties of the XXZ anisotropic ferrimagnetic spin-(1/2, 1) chain under the presence of a magnetic field using the Villain transformation method. The effect of the XXZ anisotropic parameter and external magnetic field on the thermodynamic observables are calculated at finite temperature. The energy spectra exhibit the coexistence of a gapless branch and a gapful branch, both of them are sensitive to the change of XXZ anisotropic parameter. The gapless branch exhibits a V-shape structure, while the gapful branch is reversed and presents an omega-shape for the XY model which is completely different from previous results for the XXZ model. Thermodynamic quantities such as free energy, internal energy, entropy, specific heat and magnetization are present. These findings for the isotropic case are compared with the results calculated by the other established methods and it turns out that Villain transformation well describes this system at low temperature. • The spin excitation spectrum and thermodynamic properties of the XXZ anisotropic ferrimagetic spin-(1/2, 1) chain under the presence of magnetic field are investigated by the Villain transformation method. • Two branches of the excitation energy spectra are obtained, which are sensitive to the size of the XXZ anisotropic parameter. • The gapless branch exhibits a V-shape structure, while the higher branch is reversed and exhibits an omega-shape structure for the XY model. • The dependence of the thermodynamic quantities on the XXZ anisotropic parameter and magnetic field are studied. [ABSTRACT FROM AUTHOR]