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