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  How can a Torus admit half-a flux quantum (Topological degeneracy of non-Abelian States)?

+ 4 like - 0 dislike

There is an issue that I have with the argument given in “Topological Degeneracy of non-Abelian States for Dummies” http://arxiv.org/pdf/cond-mat/0607743v2.pdf, regarding the ground state degeneracy of the Pfaffian state on a torus: This is They argue that adiabatic pairwise annihilation of quasiparticles around the x-direction (implemented by $T_x$) should be equivalent to inserting half a flux quantum into the y-direction “hole” of the torus, i.e.


Explicitly, this is described in the following paragraph, on page 9, Section 4: Consistency between non-Abelian statistics and charge fractionalization:

The issue I have with this is that the magnetic field in a vortex is localized at a point, and is not like the uniform field described by "insertion of half a flux quantum into a hole", and so the authors still have to prove that a quasiparticle encircling the appropriate fundamental cycle of the torus still picks up the same Aharanov Bohm phase, despite the fact that the magnetic fields are different in each case.

Moreover, I do not believe that it is possible for for half a flux quantum to exist: then the Chern number of the electromagnetic U(1)-bundle would be 1/2, not an integer!!!

What's going on here?

asked Dec 8, 2015 in Theoretical Physics by David B Roberts (135 points) [ revision history ]
edited Dec 8, 2015 by David B Roberts

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