Numerical simulation of non-Abelian anyons

Two-dimensional systems such as quantum spin liquids or fractional Hall exhibit anyonic excitations that possess more general statistics than bosons fermions. This exotic makes it challenging to solve even a many-body system of non-interacting anyons. We introduce an algorithm allows simulate tight-binding Hamiltonians on two-dimensional lattices. The is directly derived from the low energy topological field theory and suited for abelian non-abelian anyon models. As concrete examples, we apply study level spacing statistics, which reveals repulsion free semions, Fibonacci anyons Ising Additionally, non-equilibrium quench dynamics, where observe density distribution becomes homogeneous large times - indicating thermalization.