Lensing of Dirac monopole in Berry's phase

TL;DR

This paper explores how Berry's phase, resembling a Dirac monopole, undergoes a topology change from monopole to dipole near level crossing points, visualized as a lensing effect that displaces the effective magnetic field.

Contribution

It introduces a geometric visualization of the topology change in Berry's phase as a lensing effect causing the apparent displacement of the Dirac monopole.

Findings

Berry's phase appears as a monopole at a distance and as a dipole near level crossing.

The lensing effect causes a displacement of the effective magnetic field.

The effective magnetic field is derived from a simple geometric flux consideration.

Abstract

Berry's phase, which is associated with the slow cyclic motion with a finite period, looks like a Dirac monopole when seen from far away but smoothly changes to a dipole near the level crossing point in the parameter space in an exactly solvable model. This topology change of Berry's phase is visualized as a result of lensing effect; the monopole supposed to be located at the level crossing point appears at the displaced point when the variables of the model deviate from the precisely adiabatic movement. The effective magnetic field generated by Berry's phase is determined by a simple geometrical consideration of the magnetic flux coming from the displaced Dirac monopole.