n-Particle Quantum Statistics on Graphs
J. M. Harrison, J. P. Keating, J. M. Robbins, Adam Sawicki · Communications in Mathematical Physics · 2014
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.