Abstract
We develop a full characterization of abelian quantum statistics on graphs. We explain how the number of anyon phases is related to connectivity. For 2-connected graphs the independence of quantum statistics with respect to the number of particles is proven. For non-planar 3-connected graphs we identify bosons and fermions as the only possible statistics, whereas for planar 3-connected graphs we show that one anyon phase exists. Our approach also yields an alternative proof of the structure theorem for the first homology group of n-particle graph configuration spaces. Finally, we determine the topological gauge potentials for 2-connected graphs.
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Communicated by S. Zelditch
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Harrison, J.M., Keating, J.P., Robbins, J.M. et al. n-Particle Quantum Statistics on Graphs. Commun. Math. Phys. 330, 1293–1326 (2014). https://doi.org/10.1007/s00220-014-2091-0
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DOI: https://doi.org/10.1007/s00220-014-2091-0