Quantum Spherical Spins with Local Symmetry

Abstract

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 $C{P}^{(\mathcal{N}-1)}$ model in the limit $\mathcal{N}\to \infty$ are investigated. The dynamical generation of gauge fields is a consequence of the restoration of the local symmetry.

arXiv comment21 pages, 3 figures; References included; Several typos corrected; Accepted for publication in Phys. Rev. E

References in corpus (6)

• Quantum description of spherical spins
• Pathologies of the large-N limit for RP^{N-1}, CP^{N-1}, QP^{N-1} and mixed isovector/isotensor sigma-models
• Quantum critical point and scaling in a layered array of ultrasmall Josephson junctions
• Liquid-gas and other unusual thermal phase transitions in some large-N magnets
• Competing interactions and the Lifshitz-type Nonlinear Sigma Model
• Supersymmetric Extension of the Quantum Spherical Model

Cited by in corpus (2)

• Aspects of Emergent Symmetries
• Supersymmetric Quantum Spherical Spins with Short-Range Interactions