Effective geometric phases and topological transitions in SO(3) and SU(2) rotations

TL;DR

This paper explores how nonadiabatic dynamics induce topological phase transitions in classical and quantum magnetic moments, revealing differences in geometric phases between SO(3) and SU(2) systems and proposing experimental observations.

Contribution

It introduces the concept of an effective geometric phase associated with topological transitions in magnetic moments, highlighting differences between classical and quantum cases.

Findings

Topological phase transition driven by magnetic field topology change

Effective geometric phase identified from magnetic moment paths

Differences in geometric phase limits: 2π (classical) and π (quantum)

Abstract

We address the development of geometric phases in classical and quantum magnetic moments (spin-1/2) precessing in an external magnetic field. We show that nonadiabatic dynamics lead to a topological phase transition determined by a change in the driving field topology. The transition is associated with an effective geometric phase which is identified from the paths of the magnetic moments in a spherical geometry. The topological transition presents close similarities between SO(3) and SU(2) cases but features differences in, e.g., the adiabatic limits of the geometric phases, being $2\pi$ and $\pi$ in the classical and the quantum case, respectively. We discuss possible experiments where the effective geometric phase would be observable.