Braiding fluxes in Pauli Hamiltonian
Aharonov and Casher showed that Pauli Hamiltonians in two dimensions have gapless zero modes. We study the adiabatic evolution of these modes under the slow motion of N fluxons with fluxes Φ{sub a}∈R. The positions, r{sub a}∈R{sup 2}, of the fluxons are viewed as controls. We are interested in the holonomies associated with closed paths in the space of controls. The holonomies can sometimes be abelian, but in general are not. They can sometimes be topological, but in general are not. We analyse some of the special cases and some of the general ones. Our most interesting results concern the cases where holonomy turns out to be topological which is the case when all the fluxons are subcritical, Φ{sub a}<1, and the number of zero modes is D=N−1. If N≥3 it is also non-abelian. In the special case that the fluxons carry identical fluxes the resulting anyons satisfy the Burau representations of the braid group.
- OSTI ID:
- 22403416
- Journal Information:
- Annals of Physics (New York), Vol. 349; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
- Country of Publication:
- United States
- Language:
- English
Similar Records
Braiding statistics and link invariants of bosonic/fermionic topological quantum matter in 2+1 and 3+1 dimensions
Quantum statistics and spacetime topology: Quantum surgery formulas