Quantum critical scenario in a three-dimensional XY model with an easy-plane single-ion anisotropy via a renormalization group analysis

The low-temperature critical properties of the three-dimensional spin-1 XY model with an easy-plane single-ion anisotropy in zero magnetic field are explored on the ground of a path-integral representation and of the momentum-shell renormalization group where the single-ion anisotropy parameter drives a quantum phase transition. We address this problem first deriving systematically a suitable quantum Ginzburg-Landau-Wilson functional whose structure suggests, in a transparent way, that the microscopic spin model is equivalent to a continuous O(2)-vector one with transverse- Ising-like intrinsic dynamics (dynamic critical exponent z=1). Then, the relevant physics close to the quantum critical point is extracted from the appropriate one-loop Wilsonian flow equations. In particular we calculate the zero-temperature critical value of the anisotropy parameter for different cubic lattices. We compare our findings with those obtained in literature by means of alternative methods and of experiments on Praseodymium. The critical line ending in the quantum critical point is also calculated and the related shift exponent is determined. Finally, by solving in different asymptotic regimes the self-consistent equation for transverse susceptibility, a finite-temperature quantum critical scenario emerges which is quite similar to the conventional ones.