  Motivated by an analogy with the spin anisotropies in the quantum XY chain
and its reformulation in terms of spin-less Majorana fermions, its bosonic
analogue, the spin-anisotropic quantum spherical model, is introduced. The
exact solution of the model permits to analyse the influence of the
spin-anisotropy on the phase diagram and the universality of the critical
behaviour in a new way, since the interactions of the quantum spins and their
conjugate momenta create new effects. At zero temperature, a quantum critical
line is found, which is in the same universality class as the thermal phase
transition in the classical spherical model in $d+1$ dimensions. The location
of this quantum critical line shows a re-entrant quantum phase transition for
dimensions $1<d\lesssim 2.065$.
