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Simulation of Anyons Using Tensor Network Algorithms

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The simulation of systems of anyons offers a significant challenge to
the condensed matter physicist. These systems are presently of
substantial theoretical and experimental interest due to their potential
for universal quantum computation, but due to their non-trivial exchange
statistics, the tools available for their study have been limited. In
this talk, I will present a formalism whereby any existing tensor
network algorithm may be adapted for use with both Abelian and
non-Abelian anyons, culminating in our recent simulations of infinite
1-D chains of interacting anyons using the Multi-scale Entanglement
Renormalisation Ansatz, or MERA, demonstrating that tensor network
algorithms may be effectively employed in the study of anyonic systems.