|Description||2020 Spring Physics Colloquium Series|
Jon Harrison, Ph.D.
Department of Mathematics
Anyons on Networks
The quantum mechanics of indistinguishable particles on a surface allows for the possibility of anyons, particles whose exchange paths are associated with any phase factor rather than the plus or minus one associated with Bosons or Fermions respectively. Quasiparticles behaving as anyons appear in the fractional quantum Hall effect and non-abelian anyons have been proposed as an architecture for a topological quantum computer. We show that restricting the dimension of the space further, from a surface to a network of one-dimensional wires (a graph), expands the range of anyon behavior. The anyon properties are determined by the connectivity of the network with 3-connected networks behaving like three-dimensional space when the graph is non-planar or a two-dimensional surface when the graph is planar. A 2-connected graph can have multiple anyon phases or combine boson and fermion behavior and on 1-connected graphs the particle statistics also depends on the number of particles.