Complex magnetic monopoles and geometric phases around diabolic and exceptional points

TL;DR

This paper explores the geometric phase around diabolic and exceptional points, revealing complex magnetic monopoles and their distinct flux behaviors, with implications for open quantum systems.

Contribution

It introduces the concept of complex magnetic monopoles for geometric phases at exceptional points, extending the understanding of topological effects in quantum systems.

Findings

Geometric phase at diabolic points is flux of Dirac monopole.

At exceptional points, the geometric phase is flux of a complex magnetic monopole.

Finite gap at diabolic points; infinite gap at exceptional points.

Abstract

We study the geometric phase (GP)in presence of diabolic (DP) and exceptional (EP) points. While the GP associated with the DP is the flux of the Dirac monopole, the GP related to the EP, being complex one, is described by the flux of complex magnetic monopole. For open systems, in week-coupling limit, the leading environment-induced contribution to the real part of complex GP is given by a quadrupole term, and to its imaginary part by a dipolelike field. We find that the GP has a finite gap at the DP and infinite one at the EP.