n-particle quantum statistics on graphs

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.

34 pages, 21 figures

References in corpus (3)

• Quantum statistics on graphs
• Quantum graphs with singular two-particle interactions
• Discrete Morse functions for graph configuration spaces

Cited by in corpus (16)

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• Approximate Hofstadter- and Kapit-Mueller-like parent Hamiltonians for Laughlin states on fractals
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