Effect of biquadratic exchange on the phase diagram of a spin-1 transverse XY model with single-ion anisotropy

The two-time Green function method is employed to explore the effect of the biquadratic exchange interaction on the phase diagram of a d-dimensional spin-1 transverse XY model with single-ion anisotropy close to the magnetic-field-induced quantum critical point. We work at level of the Anderson-Callen-decoupling-like framework for both easy-plane and easy-axis single-ion anisotropy. The structure of the phase diagram is analyzed with analytical estimates and numerical calculations by adopting Tyablikov-like decouplings for the exchange higher order Green functions in the equation of motion. For dominant bilinear short-range exchange interaction the structure of the phase diagram close to the quantum critical point remains qualitatively the same of that in absence of biquadratic interaction including reentrant critical lines. When the biquadratic exchange becomes increasingly dominant its role appears more effective and tends to reduce or destroy the reentrant character of the critical lines.