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

TL;DR

This paper investigates the entanglement and statistical properties of a system of hard-core anyons on a ring, revealing how entanglement measures relate to topological features and providing analytical and numerical insights into their density matrices.

Contribution

It analytically derives the large N asymptotics of the anyonic density matrix and demonstrates the dependence of entanglement on the anyonic parameter, extending previous bosonic results.

Findings

Entanglement depends on the anyonic parameter.

Analytical large N asymptotics of the density matrix are provided.

Numerical analysis confirms the analytical results.

Abstract

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.