Braiding fluxes in Pauli Hamiltonian

Oded Kenneth

Aharonov and Casher  showed that Pauli Hamiltonians in two dimensions have gapless zero modes. We study the adiabatic evolution of these modes under slow motion of N fluxons with noninteger fluxes. The positions of the fluxons are viewed as controls. We are interested in the holonomies associated with closed paths in the space of controls.  In general these holonomies need not be topological. We show that when the number of (unconfined) zero modes is D=N-1, then fluxon braiding is topological. If N>2 it is also non-abelian. In the special case that the fluxons carry identical fluxes they can be interpreted as non abelian anyons that satisfy the Burau representations of the braid group.