Braid Group, Gauge Invariance and Topological Order

Details Braid Group, Gauge Invariance and Topological Order Braid Group, Gauge Invariance and Topological Order

2006-04-21

arxiv.org/abs/cond-mat/0604506v2

Phys. Rev. Lett. 97, 010601 (2006)

Physics

Condensed Matter

Strongly Correlated Electrons

5pages, 2 figures; reference added

Scientific paper

10.1103/PhysRevLett.97.010601

Topological order in two-dimensional systems is studied by combining the braid group formalism with a gauge invariance analysis. We show that flux insertions (or large gauge transformations) pertinent to the toroidal topology induce automorphisms of the braid group, giving rise to a unified algebraic structure that characterizes the ground-state subspace and fractionally charged, anyonic quasiparticles. Minimal ground state degeneracy is derived without assuming any relation between quasiparticle charge and statistics. We also point out that noncommutativity between large gauge transformations is essential for the topological order in the fractional quantum Hall effect.

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