Quantum phase transition in the spin-anisotropic quantum spherical model

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 $1<d\lesssim 2.065$.