Entanglement properties and moment distributions of a system of hard-core anyons on a ring

We study the one-particle von Neumann entropy of a system of N hard-core anyons on a ring. The entropy is found to have a clear dependence on the anyonic parameter which characterizes the generalized fractional statistics described by the anyons. This confirms the entanglement as a valuable measure to investigate topological properties of quantum states. Furthermore, we determine analytically the large N asymptotics of the anyonic one-particle density matrix. The formula presented here generalizes the Lenard formula obtained for a system of N hard-core bosons. Finally, we present a numerical analysis which confirms the analytical results and provides additional insight into the problem under consideration.