Quantum Spherical Spins with Local Symmetry

TL;DR

This paper introduces an exactly solvable quantum spherical spin model with local symmetry, revealing spontaneous symmetry breaking and phase transitions, and explores the emergence of gauge fields and their relation to the $CP^{( -1)}$ model.

Contribution

It constructs a novel quantum spherical spin system with local symmetry, analyzing its phase transitions and gauge field dynamics, and establishes its connection to the $CP^{( -1)}$ model.

Findings

Local symmetry is spontaneously broken at finite and zero temperatures.

The model exhibits classical and quantum phase transitions with nontrivial critical behavior.

Dynamical gauge fields are generated and related to the $CP^{( -1)}$ model.

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 $CP^{(\mathcal{N}-1)}$ 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.