Quantum Spherical Spins with Local Symmetry
  We construct a quantum system of spherical spins with a continuous local symmetry. The model is exactly soluble in the thermodynamic limit and exhibits a number of interesting properties. We show that the local symmetry is spontaneously broken at finite as well as zero temperatures, implying the existence of classical and quantum phase transitions with a nontrivial critical behavior. The dynamical generation of gauge fields and the equivalence with the $CP^{(\mathcal{N}-1)}$ model in the limit $\mathcal{N}\rightarrow\infty$ are investigated. The dynamical generation of gauge fields is a consequence of the restoration of the local symmetry. 
Pedro R. S. Gomes and P. F. Bienzobaz
hep-th cond-mat.stat-mech cond-mat.supr-con