Dr. Abhishek Roy
University of Illinois

Berry Phases in the Majorana Representation

The Majorana representation describes a general spin state as a set of points on the Bloch sphere. We use it to study Berry phases, both abelian and non-abelian, for single spin systems of high spin, such as molecular magnets.

We find that Chern numbers associated to diabolical points (level crossings) may be seen visually as the number of wrappings of Majorana points. This is a generalization of the well-known result for spin 1/2.

We also comment on applications to other Hamiltonians where topological states can be understood as constraints on the Berry phase eg. topological insulators.